Question

Mai has a jar of quarters and dimes. She takes at least 10 coins out of the jar and has less than $2,00. (Lesson 2-25) a. Write a system of inequalities that represents the number of quarters, q, and the number of dimes, d, that Mai could have. b. Is it possible that Mai has each of the following combinations of coins? If so, explain or show how you know. If not, state which constraint—the amount of money or the number of coins—it does not meet.

i. 3 quarters and 12 dimes
ii. 4 quarters and 10 dimes
iii. 2 quarters and 5 dimes

Answer 1

The system of inequalities representing the number of quarters, q, and the number of dimes, d, that Mai could have is: 0.25q + 0.10d >= 2.00 (at least 10 coins are taken out of the jar), q >= 10 (less than $2.00), and d >= 10.

Step-by-step explanation:

The correct answer is:

a. The system of inequalities representing the number of quarters, q, and the number of dimes, d, that Mai could have is:

0.25q + 0.10d ≥ 2.00 (at least 10 coins are taken out of the jar)
q ≥ 10 (less than $2.00)
d ≥ 10

b. Let's check if Mai could have each of the following combinations of coins:

i. 3 quarters and 12 dimes:
We substitute q = 3 and d = 12 into the inequalities:
0.25(3) + 0.10(12) = 0.75 + 1.20 = 1.95 < 2.00
The combination satisfies the inequalities, so it is possible.

ii. 4 quarters and 10 dimes:
We substitute q = 4 and d = 10 into the inequalities:
0.25(4) + 0.10(10) = 1.00 + 1.00 = 2.00 ≥ 2.00
The combination does not satisfy the inequalities as it is equal to $2.00, so it is not possible under the constraint of having less than $2.00.

iii. 2 quarters and 5 dimes:
We substitute q = 2 and d = 5 into the inequalities:
0.25(2) + 0.10(5) = 0.50 + 0.50 = 1.00 < 2.00
The combination satisfies the inequalities, so it is possible.