The equation a=0.45(m-450)+39.99 gives the amount a in dollars of Bruce's cell phone bill in a month when he uses m minutes of talk time.

Question

a. Last month, Bruce's bill was $53.49. How many minutes of talk time did he use?

b. This month, Bruce promises to use no more than half the number of minutes he used last month. He has already used 225 minutes. How many more talk minutes can he use this month without breaking his promise? Use an inequality to explain your reasoning.

Answer 1

A) We need to substitute $53.49 for a in the equation and solve for m.

53.49=0.45(m-450)+39.99 [subtract 39.99 from both sides]

13.50 = 0.45(m-450) [Divide both sides by 0.45]

30 = m - 450 [add 450 to both sides]

480 = m

CHECK:

13.5 = 0.45(480-450)

13.5 = .45(30)

13.5 = 13.5

B) He promised to use half the minutes of last month so 480 * .5 = 240

If he has already used 225 minutes then he can only use 240 - 225 = 15 more minutes this month