Question

Tyler filled a small jar with quarters and dimes and donated it to his school's charity club. The club member receiving the jar asked, "Do you happen to know how much is in the jar?" Tyler said, "I know it’s at least $ 8.50, but I don’t know the exact amount."

a. Write an inequality to represent the relationship between the number of dimes, d, the number of quarters, a, and the dollar amount of the money in the jar.
b. Graph the solution set to the inequality and explain what a solution means in this situation. Number of Dimes
c. Suppose Tyler knew there are 25 dimes in the jar. Write an inequality that represents how many quarters could be in the jar.

Answer 1

a. The inequality is 0.10d + 0.25a >= 8.50. b. The solution set is the region above the graph line. c. The inequality is 0.10(25) + 0.25a >= 8.50.

Step-by-step explanation:

a. The inequality to represent the relationship between the number of dimes, d, the number of quarters, a, and the dollar amount of the money in the jar is: 0.10d + 0.25a ≥ 8.50. This inequality states that the total value of the dimes (0.10d) plus the total value of the quarters (0.25a) is greater than or equal to $8.50.

b. To graph the solution set to the inequality, plot the points on a coordinate plane that satisfy the inequality. Shade the region above the graph line. In this situation, a solution means any combination of dimes and quarters that results in a total value greater than or equal to $8.50.

c. If Tyler knew there are 25 dimes in the jar, the inequality that represents how many quarters could be in the jar is: 0.10(25) + 0.25a ≥ 8.50. This inequality simplifies to: 2.5 + 0.25a ≥ 8.50. Solving for 'a' gives a ≥ (8.50 - 2.5) / 0.25, which simplifies to a ≥ 24.