Question

Sal is trying to determine which cell phone and service plan to buy for his mother. The first phone costs $100 and $55 per month for unlimited usage. The second phone costs $150 and $51 per month for unlimited usage. How many months will it take for the second phone to be less expensive than the first phone?

The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is .
The solution to the inequality is .
Sal’s mother would have to keep the second cell phone plan for at least months in order for it to be less expensive.

Answer 1

The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is

✔ 100 + 55x > 150 + 51x

.

The solution to the inequality is

✔ x > 12.5

.

Sal’s mother would have to keep the second cell phone plan for at least

✔ 13

months in order for it to be less expensive.

Explanation:

Answer 2

First phone:
f(x)= cost of the first phone
x=number of months

f(x)=55x+100

Second phone:
g(x)=cost of the second phone.
x=number of months.

g(x)=51x+150

Therefore:
The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is:

g(x)<f(x)


51x+150<55x+100

Answer: 51x+150<55x+100

The solution to the inequality is:
51x+150<55x+100
51x-55x<100-150
-4x<-50
-x<-50/4
-x<-12.5
x>12.5

Answer: x>12.5 months (x>13)

Sal’s mother would have to keep the second cell phone plan for at least months in order for it to be less expensive.

Answer: 13 months.