Problem solving strategy: guess and check problem

Question

Dave and Briana have a total of 82 CD's. Dave has 16 more CD's than Briana. How many CD's does each have?

Answer 1

Hello, Lori 

 

The first thing that we must do is set up the system of linear equations.

 

Let d represent the number of CDs that Dave has.

Let b represent the number ofCDs that Briana has

 

Further more we are told that Dave 16 more CDs that Briana, this can be represented as 

d= b+ 16

 

In addition, we are told that together they have 83 CDs. This can be expressed as

 

d+b= 82 or d= 82-b 

 

So, our system of linear equations is

d= b+16

d= 82-b

 

The best way to solve for this problem will be to make the equations equal to each other since both of them start with d=

b+16= 82-b          Add b to both sides

+b           +b

2b+16= 82

    -16    -16

2b=66                 Divide both sides by 2

b=33                   This is the number of CDs that Briana has

 

To find d, how many CDs Dave has, we are going to use 

b+d= 82

33+d= 82         Substituting 33 for b

-33      -33         Subtracting 33 from both sides

       d= 49.       This is the number of CDs that Dave has.

Well, Lori that should be our answers.  Glad to help out. Please rate my answer :)

 

D. Y. Taylor