Question

Sam 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 iphone 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?

Answer 1

13 months

Explanation:

x is the number of months

first phone:

f(x) = 55x + 100

second phone:

g(x) = 51x + 150

now set up the inequality

g(x)<f(x)

51x + 150 < 55x + 100

Solve the inequality:

51x + 150 < 55x + 100

(get everything on the correct sides... combine the like terms)

51x - 55x < 100 - 150

-4x < -50

divide both sides by -4 (don't forget to flip the inequality sign when dividing by a negative number.)

x > 50/4

x > 12.5

round up to 13

Answer 2

Here it is solve the inequality and round up when determining the number of months.

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