When Mark counted the money he collected from his paper route he had $9.75 all in quarters and dimes. The ratio of dimes to quarters was 7 : 5. How many coins of each type were there?

Answer 1

"When Mark counted the money he collected from his paper route he had $9.75 all in quarters and dimes. The ratio of dimes to quarters was 7 : 5. How many coins of each type were there?"

We can make an equation from this information.

The ratio of dimes to quarters was 7 : 5 tells us that dimes and quarter are related in the proportion

7X: 5X.

We will use 7X for the number of dimes and 5X for the number of quarter in the solution of the problem.

The value of each dime is 5 cents. The value of each quarter is 25 cents. The value of their sum ( in cents) is 975.

So the equation becomes:

( number of dimes).10 + (number of quarters).25 = 975

or

(7X). 10 + (5X).25 = 975

70X + 125X = 975

195X = 975

X = 5 ( divide both sides by 195)

recall that we are looking for the number of dimes, and that is equal to 7X

so number of dimes = 7X = 35

also, number of quarters is 5X = 25.

Answer 2

The ratio of dimes to quarters means that for every 7 dimes he also collected 5 quarters.

In math this means that

d/7 = q/5

If there was 14 dimes there will also be 1 quarters.

The sum of all the money is 975 cents and since a quarter is 25 and a dime is 10.

This equation would look like

975 = 25 * q + 10 * d

By simultaneous solving these equations you can find the amount of dimes and quarters.

Simplify the first equation

d/7 = q/5

*35 *35

5d = 7q

/5 /5

d = 7/5 q

Plug this into the other equation

975 = 25 * q + 10 * (7/5 * q)

975 = 25q + 14q

975 = 39q

/39 /39

25 = q

So there are 25 quarters.

Since there is a ratio of 7 dimes to 5 quarters

There will be 7/5 * 25 dimes

or 35 dimes

there are 25 quarters and 35 dimes

Answer 3

The ratio is 7 dimes to 5 quarters.

Start by adding 7 dimes and 5 quarters, 7(0.10) + 5(0.25) = 0.70 + 1.25 = $1.95.

Then I add 5 sets of 7 dimes and 5 sets of 5 quarters to get 35(0.10) + 25(0.25) = 3.50 + 6.25 = $9.75.

Therefore, Mark has 35 dimes and 25 quarters for a total of $9.75.

Answer 4

7*25+5*10=2.25

14 10 =4.50

21 15 =6.75

28 20 =9.00

35 25=11.25

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