Substitution word problem

Question

a student bought 1 box of crayons and 5 reams of paper for $54. She bought 5 boxes of crayons and 3 reams of paper for $50. What is the cost of each vox of crayons and each ream of paper?

Answer 1

Hi John from Odessa, FL...hope you had a great day at school today.

Glad you contacted Wyzant to help with your problem. I will help you get started, help you with setting it up, but you will be the one who will need to do the calculation. That way you will know how to set up these kind of problems.

We start by identifying and labeling each of them: 

      student buys 1 box of crayons for a certain cost, label that      1c

      student buys 5 reams of paper for a certain cost, label that     5p

      together they cost $54 so we can write it:

                  1c  +  5p  = $54

       You don't know the cost of one box of crayons as well as you don't 

       know the cost of one ream of paper.

 

The student goes out and buys 5 boxes of crayons, label that   5c

Student buys 3 reams of paper, label that                               3p

       The total cost is:

          5c  +  3p  =  $50 

 

Now we use the Substitution operation to solve the problem;

You will start with c.  Let's take the second equation:

                                    5c + 3p = $50 

                                    5c + 3p - 3p  = $50 -  3p

                                                   5c  = $50  - 3p    Cancel the 5

                                                   5            5     

 

                                                 c  =  $50  -  3p    rewrite the equation

                                                           5        5    cancel where you can

 

                                                c  =  $10  -  3p 

                                                                    5

 

Now we SUBSTITUTE the c = value into the 1st equation

 

               1c  +  5p  =  $54    re-write the equation with SUBSTITUTION

       

          1($10 - 3p) + 5p = $54      Complete the operation

                       5

 

              $10 - 3p + 5p   =  $54   Move the known value to the right side

                        5

 

    $10 - $10 - 3p + 5p  = $54 -$10    Complete the operation and rewrite                        5

 

                  5p  -  3p  =  $44        Change 5p to a fraction with common

                            5                                       denominator

 

                 25p  -  3p   =  $44         Complete the operation and rewrite

                        5

 

                     22p    =  $44      Multiply by 5(denominator) move to right

                       5

 

                  5  •  22p    =  $44 • 5  Complete operation/cancel/rewrite

                           5

 

                        22p   =   $220

Now...you have all the tools to complete the operation. Solve for p then check you answer. 

If you need any further assistance, contact me on Wyzant.

 

         

Answer 2

c = cost of crayons

p = cost of paper

 

c + 5p = 54

5c + 3p = 50

 

Using substitution:  Solve 1st equation for c

c = 54 - 5p

Substitute that into 2nd equation

 

5(54-5p) + 3p = 50

270 - 25p + 3p = 50

-22p = -220

p = 10

 

c = 54 - 5p = 54 - 50 = 4

 

ream of paper costs $10

box of crayons costs $4