Find the unit price of each item which was paid as whole












0












$begingroup$


I am trying to help my daughter in her math and there is this question I can't quite get my head around, The sum is:



Three friends go into a book shop. Salma buys a cook book and a novel, she pays $ 20.75. Isla buys the same novel and a dictionary. Her bill comes to $ 26.65. Josh buys a cook book and a Dictionary and pays $ 30.90.



What is the price of each book?






problem-solving word-problem







share|cite|improve this question











$endgroup$

















    0












    $begingroup$


    I am trying to help my daughter in her math and there is this question I can't quite get my head around, The sum is:



    Three friends go into a book shop. Salma buys a cook book and a novel, she pays $ 20.75. Isla buys the same novel and a dictionary. Her bill comes to $ 26.65. Josh buys a cook book and a Dictionary and pays $ 30.90.



    What is the price of each book?






    problem-solving word-problem







    share|cite|improve this question











    $endgroup$















      0












      0








      0





      $begingroup$


      I am trying to help my daughter in her math and there is this question I can't quite get my head around, The sum is:



      Three friends go into a book shop. Salma buys a cook book and a novel, she pays $ 20.75. Isla buys the same novel and a dictionary. Her bill comes to $ 26.65. Josh buys a cook book and a Dictionary and pays $ 30.90.



      What is the price of each book?






      problem-solving word-problem







      share|cite|improve this question











      $endgroup$




      I am trying to help my daughter in her math and there is this question I can't quite get my head around, The sum is:



      Three friends go into a book shop. Salma buys a cook book and a novel, she pays $ 20.75. Isla buys the same novel and a dictionary. Her bill comes to $ 26.65. Josh buys a cook book and a Dictionary and pays $ 30.90.



      What is the price of each book?






      problem-solving word-problem




      problem-solving word-problem






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Dec 10 '18 at 8:27









      Arthur

      115k7116198




      115k7116198










      asked Dec 10 '18 at 8:25









      PremPrem

      31




      31






















          2 Answers
          2






          active

          oldest

          votes


















          0












          $begingroup$

          Hint: Setting $C=$ price of cook book; $N=$price of novel and $D=$price of dictionary, we get the equations
          $$
          left{
          begin{array}{crccc}
          C& + N & & = &20.75\
          & N & + D & = & 26.65 \
          C &&+D &=& 30.90
          end{array}
          right.
          $$
          This is fairly easy to solve. Adding the first and last equations together, we obtain
          $$
          left{
          begin{array}{crccc}
          2C& + N & +D & = &51.65\
          & N & + D & = & 26.65 \
          end{array}
          right.
          $$
          From which we can easily see (by subtracting the equations from each other) that
          $$
          2C = 25.00 qquad Rightarrow qquad C = 12.50
          $$
          now we can plug in this value to the original last equation, and we obtain $D = 30.90 - 12.50 = 18.40$. Similarly, plugging this result in the second equation of the original set, we get $N=26.65 - 18.40 = 8.25$



          The final answers are therefore
          $$
          C = 12.50 qquad N = 8.25 qquad D = 18.40
          $$






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            Actually I don't know how to work out the answer. Also can you advise where I can find similar sums online?
            $endgroup$
            – Prem
            Dec 10 '18 at 8:37










          • $begingroup$
            About finding similar stuff online: I don't have any recommendations right now, but I would advise googling "solving systems of linear equations".
            $endgroup$
            – Matti P.
            Dec 10 '18 at 9:03










          • $begingroup$
            Matti P. Thank you so much for the prompt response, more than the answer I was keen to know about the process to achieving the answer. This helps a great deal. Gold bless.
            $endgroup$
            – Prem
            Dec 10 '18 at 9:20



















          0












          $begingroup$

          I'll try to put it in a way, so you may explain it to your daughter.



          Let's denote $C$ price for cook book, $N$ novel, $D$ dictionary.



          So you have
          $C + N = 20.75$, $N + D = 20.65$ and $C + D = 30.90$.
          Now the cost of buying a cook book and selling a dictionary $ C - D = C + N - (N + D) = 20.75 -20.65 = 0.10$. And finally buying two cookbooks: $2C = 2C - D + D = C + D + (C - D) = 30.90 + 0.10 = 31.00$. So $C = 15.50$. The rest should by easy.






          share|cite|improve this answer









          $endgroup$













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            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            0












            $begingroup$

            Hint: Setting $C=$ price of cook book; $N=$price of novel and $D=$price of dictionary, we get the equations
            $$
            left{
            begin{array}{crccc}
            C& + N & & = &20.75\
            & N & + D & = & 26.65 \
            C &&+D &=& 30.90
            end{array}
            right.
            $$
            This is fairly easy to solve. Adding the first and last equations together, we obtain
            $$
            left{
            begin{array}{crccc}
            2C& + N & +D & = &51.65\
            & N & + D & = & 26.65 \
            end{array}
            right.
            $$
            From which we can easily see (by subtracting the equations from each other) that
            $$
            2C = 25.00 qquad Rightarrow qquad C = 12.50
            $$
            now we can plug in this value to the original last equation, and we obtain $D = 30.90 - 12.50 = 18.40$. Similarly, plugging this result in the second equation of the original set, we get $N=26.65 - 18.40 = 8.25$



            The final answers are therefore
            $$
            C = 12.50 qquad N = 8.25 qquad D = 18.40
            $$






            share|cite|improve this answer











            $endgroup$













            • $begingroup$
              Actually I don't know how to work out the answer. Also can you advise where I can find similar sums online?
              $endgroup$
              – Prem
              Dec 10 '18 at 8:37










            • $begingroup$
              About finding similar stuff online: I don't have any recommendations right now, but I would advise googling "solving systems of linear equations".
              $endgroup$
              – Matti P.
              Dec 10 '18 at 9:03










            • $begingroup$
              Matti P. Thank you so much for the prompt response, more than the answer I was keen to know about the process to achieving the answer. This helps a great deal. Gold bless.
              $endgroup$
              – Prem
              Dec 10 '18 at 9:20
















            0












            $begingroup$

            Hint: Setting $C=$ price of cook book; $N=$price of novel and $D=$price of dictionary, we get the equations
            $$
            left{
            begin{array}{crccc}
            C& + N & & = &20.75\
            & N & + D & = & 26.65 \
            C &&+D &=& 30.90
            end{array}
            right.
            $$
            This is fairly easy to solve. Adding the first and last equations together, we obtain
            $$
            left{
            begin{array}{crccc}
            2C& + N & +D & = &51.65\
            & N & + D & = & 26.65 \
            end{array}
            right.
            $$
            From which we can easily see (by subtracting the equations from each other) that
            $$
            2C = 25.00 qquad Rightarrow qquad C = 12.50
            $$
            now we can plug in this value to the original last equation, and we obtain $D = 30.90 - 12.50 = 18.40$. Similarly, plugging this result in the second equation of the original set, we get $N=26.65 - 18.40 = 8.25$



            The final answers are therefore
            $$
            C = 12.50 qquad N = 8.25 qquad D = 18.40
            $$






            share|cite|improve this answer











            $endgroup$













            • $begingroup$
              Actually I don't know how to work out the answer. Also can you advise where I can find similar sums online?
              $endgroup$
              – Prem
              Dec 10 '18 at 8:37










            • $begingroup$
              About finding similar stuff online: I don't have any recommendations right now, but I would advise googling "solving systems of linear equations".
              $endgroup$
              – Matti P.
              Dec 10 '18 at 9:03










            • $begingroup$
              Matti P. Thank you so much for the prompt response, more than the answer I was keen to know about the process to achieving the answer. This helps a great deal. Gold bless.
              $endgroup$
              – Prem
              Dec 10 '18 at 9:20














            0












            0








            0





            $begingroup$

            Hint: Setting $C=$ price of cook book; $N=$price of novel and $D=$price of dictionary, we get the equations
            $$
            left{
            begin{array}{crccc}
            C& + N & & = &20.75\
            & N & + D & = & 26.65 \
            C &&+D &=& 30.90
            end{array}
            right.
            $$
            This is fairly easy to solve. Adding the first and last equations together, we obtain
            $$
            left{
            begin{array}{crccc}
            2C& + N & +D & = &51.65\
            & N & + D & = & 26.65 \
            end{array}
            right.
            $$
            From which we can easily see (by subtracting the equations from each other) that
            $$
            2C = 25.00 qquad Rightarrow qquad C = 12.50
            $$
            now we can plug in this value to the original last equation, and we obtain $D = 30.90 - 12.50 = 18.40$. Similarly, plugging this result in the second equation of the original set, we get $N=26.65 - 18.40 = 8.25$



            The final answers are therefore
            $$
            C = 12.50 qquad N = 8.25 qquad D = 18.40
            $$






            share|cite|improve this answer











            $endgroup$



            Hint: Setting $C=$ price of cook book; $N=$price of novel and $D=$price of dictionary, we get the equations
            $$
            left{
            begin{array}{crccc}
            C& + N & & = &20.75\
            & N & + D & = & 26.65 \
            C &&+D &=& 30.90
            end{array}
            right.
            $$
            This is fairly easy to solve. Adding the first and last equations together, we obtain
            $$
            left{
            begin{array}{crccc}
            2C& + N & +D & = &51.65\
            & N & + D & = & 26.65 \
            end{array}
            right.
            $$
            From which we can easily see (by subtracting the equations from each other) that
            $$
            2C = 25.00 qquad Rightarrow qquad C = 12.50
            $$
            now we can plug in this value to the original last equation, and we obtain $D = 30.90 - 12.50 = 18.40$. Similarly, plugging this result in the second equation of the original set, we get $N=26.65 - 18.40 = 8.25$



            The final answers are therefore
            $$
            C = 12.50 qquad N = 8.25 qquad D = 18.40
            $$







            share|cite|improve this answer














            share|cite|improve this answer



            share|cite|improve this answer








            edited Dec 10 '18 at 8:50

























            answered Dec 10 '18 at 8:34









            Matti P.Matti P.

            2,0381414




            2,0381414












            • $begingroup$
              Actually I don't know how to work out the answer. Also can you advise where I can find similar sums online?
              $endgroup$
              – Prem
              Dec 10 '18 at 8:37










            • $begingroup$
              About finding similar stuff online: I don't have any recommendations right now, but I would advise googling "solving systems of linear equations".
              $endgroup$
              – Matti P.
              Dec 10 '18 at 9:03










            • $begingroup$
              Matti P. Thank you so much for the prompt response, more than the answer I was keen to know about the process to achieving the answer. This helps a great deal. Gold bless.
              $endgroup$
              – Prem
              Dec 10 '18 at 9:20


















            • $begingroup$
              Actually I don't know how to work out the answer. Also can you advise where I can find similar sums online?
              $endgroup$
              – Prem
              Dec 10 '18 at 8:37










            • $begingroup$
              About finding similar stuff online: I don't have any recommendations right now, but I would advise googling "solving systems of linear equations".
              $endgroup$
              – Matti P.
              Dec 10 '18 at 9:03










            • $begingroup$
              Matti P. Thank you so much for the prompt response, more than the answer I was keen to know about the process to achieving the answer. This helps a great deal. Gold bless.
              $endgroup$
              – Prem
              Dec 10 '18 at 9:20
















            $begingroup$
            Actually I don't know how to work out the answer. Also can you advise where I can find similar sums online?
            $endgroup$
            – Prem
            Dec 10 '18 at 8:37




            $begingroup$
            Actually I don't know how to work out the answer. Also can you advise where I can find similar sums online?
            $endgroup$
            – Prem
            Dec 10 '18 at 8:37












            $begingroup$
            About finding similar stuff online: I don't have any recommendations right now, but I would advise googling "solving systems of linear equations".
            $endgroup$
            – Matti P.
            Dec 10 '18 at 9:03




            $begingroup$
            About finding similar stuff online: I don't have any recommendations right now, but I would advise googling "solving systems of linear equations".
            $endgroup$
            – Matti P.
            Dec 10 '18 at 9:03












            $begingroup$
            Matti P. Thank you so much for the prompt response, more than the answer I was keen to know about the process to achieving the answer. This helps a great deal. Gold bless.
            $endgroup$
            – Prem
            Dec 10 '18 at 9:20




            $begingroup$
            Matti P. Thank you so much for the prompt response, more than the answer I was keen to know about the process to achieving the answer. This helps a great deal. Gold bless.
            $endgroup$
            – Prem
            Dec 10 '18 at 9:20











            0












            $begingroup$

            I'll try to put it in a way, so you may explain it to your daughter.



            Let's denote $C$ price for cook book, $N$ novel, $D$ dictionary.



            So you have
            $C + N = 20.75$, $N + D = 20.65$ and $C + D = 30.90$.
            Now the cost of buying a cook book and selling a dictionary $ C - D = C + N - (N + D) = 20.75 -20.65 = 0.10$. And finally buying two cookbooks: $2C = 2C - D + D = C + D + (C - D) = 30.90 + 0.10 = 31.00$. So $C = 15.50$. The rest should by easy.






            share|cite|improve this answer









            $endgroup$


















              0












              $begingroup$

              I'll try to put it in a way, so you may explain it to your daughter.



              Let's denote $C$ price for cook book, $N$ novel, $D$ dictionary.



              So you have
              $C + N = 20.75$, $N + D = 20.65$ and $C + D = 30.90$.
              Now the cost of buying a cook book and selling a dictionary $ C - D = C + N - (N + D) = 20.75 -20.65 = 0.10$. And finally buying two cookbooks: $2C = 2C - D + D = C + D + (C - D) = 30.90 + 0.10 = 31.00$. So $C = 15.50$. The rest should by easy.






              share|cite|improve this answer









              $endgroup$
















                0












                0








                0





                $begingroup$

                I'll try to put it in a way, so you may explain it to your daughter.



                Let's denote $C$ price for cook book, $N$ novel, $D$ dictionary.



                So you have
                $C + N = 20.75$, $N + D = 20.65$ and $C + D = 30.90$.
                Now the cost of buying a cook book and selling a dictionary $ C - D = C + N - (N + D) = 20.75 -20.65 = 0.10$. And finally buying two cookbooks: $2C = 2C - D + D = C + D + (C - D) = 30.90 + 0.10 = 31.00$. So $C = 15.50$. The rest should by easy.






                share|cite|improve this answer









                $endgroup$



                I'll try to put it in a way, so you may explain it to your daughter.



                Let's denote $C$ price for cook book, $N$ novel, $D$ dictionary.



                So you have
                $C + N = 20.75$, $N + D = 20.65$ and $C + D = 30.90$.
                Now the cost of buying a cook book and selling a dictionary $ C - D = C + N - (N + D) = 20.75 -20.65 = 0.10$. And finally buying two cookbooks: $2C = 2C - D + D = C + D + (C - D) = 30.90 + 0.10 = 31.00$. So $C = 15.50$. The rest should by easy.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Dec 10 '18 at 8:38









                denklodenklo

                4357




                4357






























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