Question

Thomas has $6.35 in dimes and quarters. The number of dimes is three more than three times the number of quarters. How many quarters does he have?

If q represents the number of quarters, then which of the following expressions represents the value of the number of dimes in cents?

3q + 3
6.35 - q
10(3q + 3)

Answer 1

I think the first one is correct because it is exactly what the problem stated: 3 quarters (q) +3

Answer 2

A: Thomas has 11 quarters.

B. Option C is the correct answer.

Explanation:

Let q represents the number of quarters.

Let d represents the number of dimes.

Thomas has $6.35 in dimes and quarters.

1 dime= $0.10

1 quarter= $0.25

We get the equation:

`0.10d+0.25q=6.35` ......(1)

The number of dimes is three more than three times the number of quarters. Equation forms:

`d=3+3q` ......(2)

Substituting the value of d in (1)

`0.10(3+3q)+0.25q=6.35`

=>
`0.30+0.30q+0.25q=6.35`

=>
`0.55q=6.35-0.30`

=>
`0.55q=6.05`

=> q = 11

And
`d=3+3(11)`

=> d = 36

Hence, Thomas has 11 quarters.

To know the expression that represents the value of the number of dimes in cents, we will multiply the number of dimes by 10 as 1 dime = 10 cents

`d=10*(3+3q)`

=>
`d=10(3+3q)`

So, option C is correct.