Question

A man has 14 coins in his pocket, all of which

are dimes and quarters. If the total value of his change is

$2.75, how many dimes and how many quarters does he have?

Short answer

For the given value of coins problem the number of dimes with the man is 5 and the number of quarters is 9.

Step-by-step solution

Step 1. Given information.

d = number of dimes.

q = number of quarters.

Step 2. Write down the concept.

The man has total 14 coins

We can write

d + q =14 …….(1)

Also, the total change the man has is 2.75 dollars = 275 cents.

As, each dime is 10 cents and each quarter is 25 cents.

That is,

10d + 25q = 275 ……..(2)

Step 3. Determining the values

Now, to use the elimination method to solve the equations, we multiply the first equation by 10 and subtract (2) from it, to get

10d + 10q = 140

-(10d + 25q = 275)

Solving, we get

-15q = -135

q = 9

Substituting in (1), we get

d + 9 =14

d = 14 - 9

d = 5