A farm stand sells apples, a for $4 a bucket, peaches, p, for $6 a bucket, and
strawberries, s for $9 a bucket. The stand earned $258 revenue last month.
The stand sold half as many strawberry buckets as peach buckets, and 8
fewer apple buckets than peach buckets. Using the substitution method, how
many apples, peaches, and strawberries did the farm stand sell?
O
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A. a = 12; p = 20; s = 10
a = 10; p= 20; s = 12
a = 20; p= 12; s = 10
D. a = 4; p = 6; s = 9
SUBMIT

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

According to the question,

Number of apple buckets = a.

Amount of money earned by selling apple buckets = 4a.

Number of peach buckets = p.

Amount of money earned by selling peach buckets = 6p.

Number of strawberry buckets = s.

Amount of money earned by selling strawberry buckets = 9s.

4a + 6p + 9s = 258.00

Half as many strawberry buckets as peach buckets: s = ½p

8 fewer apple buckets than peach buckets: a = p - 8

Substitution:

4(p - 8) + 6p + 9(½p) = 258.00

Solve for p

4p - 32 + 6p + 9p/2 = 258

10p + 9p/2 = 258 + 32

20p + 9p/2 = 290

29p/2 = 290

29p = 290 × 2

p = 290 ×2/29

p = 10 × 2

p = 20

8 fewer apple buckets than peach buckets:

a = p - 8

a = 20 - 8

a = 12

Half as many strawberry buckets as peach buckets:

s = ½p

s = ½ × 20

s = 10

Hence, The number of apples, peaches, and strawberries is a = 12, p = 20 and s = 10

Learn more about substitution method from here

https://brainly.in/question/19563391

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