Suppose you have just enough money, in coins, to pay for a gallon of milk priced at $2.40. You have 12 coins, all quarters and dimes. Let q equal the number of quarters and d equal the number of dimes. Which system models the given information?

The answer is

q + d = 12

0.25q + 0.10d = 2.40

q - the number of quarters

d - the number of dimes

You have 12 coins, all quarters and dimes:

q + d = 12

The value of 1 quarter is $0.25.

The value of 1 dime is $0.10.

Therefore, if you want to pay $2.40 you will have q quarters of value $0.25 (0.25q) and d dimes of value $0.10d (0.10d).

The second equation is:

0.25q + 0.10d = 2.40