Question

Beatrice has at least one quarter, one dime, one nickel, and one penny. She has exactly 13 coins total. Beatrice also has a total value of 92 cents. How many different sets of coins can she have?

Answer 1

Answer:

(Q, D, N, P) = (0, 7, 4, 2) or (1, 3, 7, 2)

Step-by-step explanation:

Let the numbers of coins be Q, D, N, P

We have:

Q + D + N + P = 13

25Q + 10D + 5N + P = 92

Obviously, P = 2, so

Q + D + N = 11         (1)

25Q + 10D + 5N = 90

Divide by 5 and get

5Q + 2D + N = 18      (2)

(2) - (1), get

4Q + D = 7

Let D = 7, Q = 0, from (1), N = 4, so the set is (Q, D, N, P) = (0, 7, 4, 2)

Let D = 3, Q = 1, from (1), N = 7, so the set is (Q, D, N, P) = (1, 3, 7, 2)

If D = 6, 5, 4, 2, 1, 0, Q is not an integer, these can be ignored.