Steve puts only dimes and quarters into his piggy bank. Right now he has five more dimes than quarters there, and they make $74.35. How many quarters and how many dimes are there in Steve's piggy bank?

There are 211 quarters and 216 dimes

Explanation:

To answer this question, we need to properly understand what a dime is and what a quarter is. A quarter is 25 cents while a dime is 10 cents in value.

Let the number of dimes present be d and the number of quarters present be q.

We are told that he has 5 more dimes than quarters.

Mathematically, this means that:

d - q = 5 or d = q + 5 ... (I)

The total value there is $74.35. In cents, this has a value of 7435 cents.

Mathematically:

25q + 10d = 7435 ... (ii)

We substitute what we have in 1 in 2

25q + 10 (q+5) = 7435

25q + 10q + 50 = 7435

35q + 50 = 7435

35q = 7435-50

35q = 7385

q = 7385/35

q = 211

Recall, d = q + 5; d = 211 + 5 = 216

Quarters, $52.75

Dimes, $21.6

Explanation:

For easy solving, we are to assume.

Let number of quarters = x

Let number of dimes = x+5

(it should be noted that this isn't the price, but the number of each. In numerals, essentially)

0.10 (x+5) + 0.25x = 74.35

0.10x+0.50+0.25x = 74.35

0.35x = 73.85, adding moving terms and then dividing both sides by 0.35

x = 211 quarters, which is $52.75

x+5 = 216 dimes, which is $21.60

To cross check our answer, we add $52.75 + $21.60 =

The total is $74.35