Question

Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting

x represent the number of nickels and
y represent the number of quarters. How many quarters did Marcos have?
a. 6
b. 7
c. 8
d. 9

Answer 1

Marcos had a total of 9 quarters. A system of equations was used to determine that he had 6 nickels and 9 quarters in a collection of 15 coins.

Step-by-step explanation:

To determine how many quarters Marcos had, we can use a system of equations based on the information provided: Marcos had a total of 15 coins consisting of nickels (x) and quarters (y), and he had 3 more quarters than nickels.

The system of equations can be written as:

• x + y = 15 (total number of coins)
• y = x + 3 (3 more quarters than nickels)

To solve for y, which represents the number of quarters, we can substitute the second equation into the first:

1. x + (x + 3) = 15
2. 2x + 3 = 15
3. 2x = 12
4. x = 6 (number of nickels)
5. y = 6 + 3
6. y = 9 (number of quarters)

So Marcos had 9 quarters.