Question

If Diego has 3 times as many quarters as nickels and they have a combined value of 560 cents, how many of each coin does he have?

A) 8 quarters, 2 nickels
B) 9 quarters, 3 nickels
C) 10 quarters, 4 nickels
D) 11 quarters, 5 nickels

Answer 1

Diego has 7 nickels and 21 quarters.

Step-by-step explanation:

Let's say the number of nickels Diego has is 'x'. Since he has 3 times as many quarters as nickels, the number of quarters he has will be 3x.

The value of a nickel is 5 cents and the value of a quarter is 25 cents. So, the total value of the nickels will be 5x cents and the total value of the quarters will be 25(3x) = 75x cents.

We are given that the combined value of all the coins is 560 cents. Therefore, we can set up the equation 5x + 75x = 560 to find the value of 'x'.

Simplifying the equation, we get 80x = 560.

Dividing both sides by 80, we find that x = 7.

Since 'x' represents the number of nickels, Diego has 7 nickels. And since he has 3 times as many quarters, he has 3(7) = 21 quarters.

Therefore, the correct answer is option D) 11 quarters, 5 nickels.