CCSS.HSA.CED.A.3.Q.A1.GLI.22 - 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." Write an inequality to represent the relationship between the number of dimes, , the number of quarters, , and the dollar amount of the money in the jar. Graph the solution set to the inequality and explain what a solution means in this situation. Suppose Tyler knew there are 25 dimes in the jar. Write an inequality that represents how many quarters could be in the jar.

Sangeetha Pulapaka (last edited 1 year ago) (Expert, Educator @Qalaxia)

The inequality to represent the amount will be 0.1 d + 0.25 q \geq 8.50, where d represents the number of dimes, q represents the number of quarters, and 8.50 represents the total money in the jar.
The solution means that the number of dimes and the number of quarters together are equal to or worth more than $8.50.
The inequality that represents the number of quarters in the jar, can be got by solving the above inequality for q, 0.1 d + 0.25 q \geq 8.50 can be written as q \geq \frac{8.5 - 2.5}{0.25} or q \geq \frac{8.5}{0.25} or q \geq 24.