Question

Kat has 19 coins, all quarters and dimes, that are worth a total of $4. The system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown. q + d = 19 0.25q + 0.1d = 4 How many quarters does she have?

Answer 1

The answer is 14 because 14*.25 = 3.50 and that leaves 5*.1=.5 add them together and you get $4.

Answer 2

Answer: She has 14 quarters.

Explanation:

Let q be the number of quarters and d be the number of dimes.

The given system of equations:

`q + d=19...........................(1)\\\\0.25q + 0.1d=4..........................(2)`

Multiplying equation (2) by 10 , we get

`2.5q+d=40.................(3)`

Subtract equation (1) from (3), we get

`1.5q=21\\\\\Rightarrow\ q=14`

Hence, she has 14 quarters.