Math world problem. Algebra 2

Question

Three boxes of cookies are labelled A, B, and C. Its known that boxes A and B together contain 35 cookies, boxes A and C contain 28 cookies, and boxes B and C contain 37 cookies. How many cookies are in each box?

 

** Please try to show work in your answer. 

Answer 1

A + B = 35

A + C = 28

B + C = 37

 

Subtract the second from the first

 

B - C = 7     Add this to the third

 

2B = 44

B = 22

 

Calculate the number in A and C.

Answer 2

Same problem using different numbers:

 

Box A + B = 49 cookies

 

Box A + C = 42 cookies

 

Box B + C = 51 cookies

 

 

If A + B = 49, then B = 49 - A or A = 49 - B

 

If A + C = 42, then A = 42 - C or C = 42 - A

 

If B + C = 51, then B = 51 - C or C = 51 - B

 

 

So, C = 42 - A or 51 - B

• Then, 42 - A = 51 - B
• Since B = 49 - A, then 42 - A = 51 - (49 - A)
• So, 42 - A = 51 - 49 + A
• Then, 42 + (49) - A + (A) = 51 - 49 + (49) + A + (A)
• So, 42 + 49 = 51 + 2A
• Since 42 + 49 = 91, then 51 + 2A = 91
• To find A, first subtract 51 from 91.
• For example, 2A = 91 - 51, so 2A = 40
• If 2A = 40, then A = 40 / 2 = 20

 

So, A = 20

 

If A = 20, and A + B = 49, then B = 49 - A, which means B = 49 - 20, and so B = 29

 

If A = 20, and A + C = 42, then 20 + C = 42, and C = 42 - 20 = 22

 

As a check:

• If C = 22, and B + C = 51, then B + 22 = 51, but B = 51 - 22, then B = 29