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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)

Verified Answer :

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

Answer:

A: Thomas has 11 quarters.

B. Option C is the correct answer.

Step-by-step 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

\(d=10\times(3+3q)\)

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

So, option C is correct.

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