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.

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:

a. $150 + 51x < 100 + 55x$

b. $x > 12.5$

c. At least 13 months

Step-by-step explanation:

Given

First Phone;

$Cost = \$100$

$Additional = \$55$ (monthly)

Second Phone;

$Cost = \$150$

$Additional = \$51$ (monthly)

Solving (a): The inequality

Represent the number of months with x

The first phone is expressed as:

$100 + 55x$

The second phone is expressed as:

$150 + 51x$

For the second to be less expensive that the first, the inequality is:

$150 + 51x < 100 + 55x$

Solving (b): Inequality Solution

$150 + 51x < 100 + 55x$

Collect Like Terms

$51x-55x$

$-4x$

Solve for x

$x > -50/-4$

$x > 12.5$

Solving (c): Interpret the solution in (b)

$x > 12.5$ implies 13, 14, 15....

Hence, She'll keep the second phone for a period of at least 13 months

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