Question

2 Points

Suppose you buy 6 buckets of apples and 4 buckets of peaches for $42. If

you bought 8 buckets of apples and 2 buckets of peaches, you would have

spent $36. How much is one bucket of apples (a), and one bucket of peaches

(p)?

A. a = $3, p = $6

B. a = $8, p = $2

C. a = $6, p = $4

D. a = $6, p = $3

SUBMIT

Answer 1

A. a = $3, p = $6

Explanation:

Let the cost of a bucket of apple=a

Let the cost of a bucket of peaches=p

6 buckets of apples and 4 buckets of peaches costs $42.

• 6a+4p=42

8 buckets of apples and 2 buckets of peaches costs $36.

• 8a+2p=36 (Multiply by 2 to make the coefficient of p 4)

• 16a+4p=72

We solve the two resulting equations simultaneously

6a+4p=42

16a+4p=72

Subtract

-10a=-30

Divide both sides by -10

a=$3

Next, we substitute a=$3 in any of the equation to solve for p

6a+4p=42

6(3)+4p=42

4p=42-6(3)

4p=42-18

4p=24

Divide both sides by 4

p=$6

Therefore, a bucket of apple costs $3 and a bucket of peaches costs $6.