Digital PSAT Math Practice Question 228: Answer and Explanation

Question: 228

David has two quarters (25 cents each) for every five dimes (10 cents each) in his change dish, with no other coins present. If he has a total of $2 in coins in the dish, how many total coins does he have?

Correct Answer: 14

Explanation:

(14) For this problem, you need to create a system of equations. First, having 2 quarters for every 5 dimes means that the ratio of quarters to dimes is .

Next, you need to come up with an expression that represents the value of the coins. Because quarters are worth 25 cents, the number of cents David has from q quarters will be 25q. Similarly, the number of cents he has from d dimes will be 10d. Because these expressions are in cents, you need the amount of money he has to also be in cents. There are 100 cents in 1 dollar, so he has 200 cents. Therefore 25q + 10d = 200. Since , you have that . Next, plug this in for q in the second equation:

. Combine the d terms: 20d = 200 → d = 10

Thus, there are 10 dimes. Plug 10 in for d in the equation that expresses q in terms of d:

Thus, there are 4 quarters and 10 dimes, giving David 14 coins total.