James sells two types of cupcakes. A basic chocolate cupcake is $2,75. His speciality chocolate covered strawberry cupcake is $3.75. He knows that he sold 185 cupcakes over the weekend and made $586.75, but he lost the paper that told him how many of each type of cupcake he sold. How many chocolate cupcakes and chocolate covered strawberry cupcakes
did he sell over the weekend?

107 chocolate cupcakes sold

78 chocolate covered strawberry cupcakes sold

Step-by-step explanation:

to solve one of these questions, you need to write two equations and then substitute back and forth to get the answer.

to start, we need to write an equation.

2.75c+3.75s=586.75

and c+s=185

reworking the second equation to isolate s, we'll then substitute it into the first one.

so s=185-c

2.75c+3.75(185-c)=586.75

2.75c+693.75-3.75c=586.75

combine like terms (the ones with a c variable attachment)

2.75c-3.75c=-1c

693.75-1c=586.75

-693.75

-107=-1c

/-1

107=c

put that back into the second equation

107+s=185

78=s

∠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.

a. she will receive a refund of $278.

step-by-step explanation: