Question

Maria has $6.35 in change in her pocket, all in nickels and quarters. She has 59 coins in all. How many quarters does she have?

a) 23
b) 25
c) 27
d) 29

Answer 1

Maria has 17 quarters.

Step-by-step explanation:

To determine the number of quarters that Maria has, we can set up a system of equations. Let's represent the number of quarters as q and the number of nickels as n. We are given two pieces of information: the total amount of change is $6.35 and the total number of coins is 59. The value of a quarter is 25 cents and the value of a nickel is 5 cents. So, we can write two equations:

1. 25q + 5n = 635 (since each quarter is worth 25 cents and each nickel is worth 5 cents)
2. q + n = 59 (since the total number of coins is 59)

Next, we can solve this system of equations using any method of our choice. Let's solve it by substitution. We'll solve equation 2 for n and substitute it into equation 1:

1. n = 59 - q
2. 25q + 5(59-q) = 635
3. 25q + 295 - 5q = 635
4. 20q + 295 = 635
5. 20q = 340
6. q = 17

Therefore, Maria has 17 quarters. The correct answer is a) 17.