A farmstand sells apples, a, for $4 a bucket; peaches, p, for $6 A bucket; and strawberries, s, for $9 a bucket. The stand earn $229 in revenue last month. The stand sold half as many strawberry buckets as peach buckets, and eight were apple buckets then peach buckets. Using the substitution method how many apples peaches and strawberries did the farmstand sell? A. a=10; p=18; s=9
B. a=4; p=6; s=9
C. a=18; p=10; s=9
D. a=9; p=18; s=10

A.

Step-by-step explanation:

a=10; p=18; s=9

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.