Final answer:
Anne has 5 quarters, 3 dimes, and 6 nickels in her coin purse to make up $1.85, based on the relationships that there are 2 less dimes than quarters and 1 more nickel than quarters.
Step-by-step explanation:
Anne has $1.85 in a coin purse. We are given that there are 2 less dimes than quarters, and 1 more nickel than quarters. To solve this problem, we need to set up equations based on the values of quarters (25 cents), dimes (10 cents), and nickels (5 cents) and the relationships between the numbers of each coin. Let's define the number of quarters as q, dimes as d, and nickels as n.
According to the problem:
- d = q - 2 (2 less dimes than quarters)
- n = q + 1 (1 more nickel than quarters)
Then the total amount in cents would be:
25q + 10d + 5n = 185
Replacing d and n with q:
25q + 10(q - 2) + 5(q + 1) = 185
Simplifying:
25q + 10q - 20 + 5q + 5 = 185
40q - 15 = 185
40q = 200
q = 5
So Anne has 5 quarters. Now we can find the number of dimes and nickels:
d = 5 - 2
d = 3 (dimes)
n = 5 + 1
n = 6 (nickels)
Anne has 5 quarters, 3 dimes, and 6 nickels.