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?
a. 3q + 3
b. 6.35 - q
c. 10(3q + 3)

Answer 1

a). Number of quarters = 11

b). Option C.

Explanation:

a). Let Thomas has number of dimes = d

and number of quarters = q

It is given that he has the number of dimes 3 more than the three times the number of quarters.

d = 3q + 3 ------(1)

Thomas has $6.35 in dimes and quarter.

Value of dimes = 0.10d

Value of quarters = 0.25q

0.10d + 0.25q = 6.35

10d + 25q = 635

2d + 5q = 127 ------(2)

We place the value of d from equation (1) in equation (2).

2(3q + 3) + 5q = 127

6q + 6 + 5q = 127

11q + 6 = 127

11q = 121

q = 11

Number of quarters are 11.

b). Since 1 dime = 10 cents

Therefore, from equation (1),

d = 10(3q + 3)

Option C is the answer.

Answer 2

Let

d---------> the number of dimes

q--------> the number of quarters

we know that

`1\ dime=\$0.10`

`1\ quarter=\$0.25`

`0.10d+0.25q=6.35` -------> equation
`1`

`d=3+3q` ------>
`q=(d-3)/3` -------> equation
`2`

substitute equation
`2` in equation
`1`

`0.10d+0.25*[(d-3)/3]=6.35`

Multiply by
`3` both sides

`0.30d+0.25*[(d-3)]=19.05`

`0.30d+0.25d-0.75=19.05`

`0.55d=19.80`

`d=36\ dimes`

find the value of q

`q=(36-3)/3`

`q=11\ quarters`

therefore

the answer Part a) is

The number of quarters is
`11`

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

we know that

the number of dimes is equal to
`d=3+3q`

and remember that

`1\ dime=\$0.10=10\ cents`

so

Multiply the number of dimes by
`10`

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

therefore

the answer part b)

the expression is the option c

`10(3+3q)`