Carrie has 40 more nickels than Joan has dimes. They both have the same amount of money. How many coins does each girl have? What is their total amount of money?

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

Step-by-step explanation:

Let be and the amounts of nickels and dimes that Carrie and Joan have, as the total amount of money that both Carrie and Joan have. A nickel is a five cent coin and a dime is a ten cent coin.

The following equations are constructed after a careful reading on statement:

Carrie's amount of money:

(Eq. 1)

Joan's amount of money:

(Eq. 2)

Relation between amounts of coins:

(Eq. 3)

First we eliminate by equalizing (Eq. 1) and (Eq. 2):

Then, we reduce the resulting formula by (Eq. 3):

And rest of variable are now determined:

Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.

∠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.