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?

Question

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
.

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.

Answer 1

To find out how many months it will take for the second phone plan to be less expensive than the first phone plan, we need to set up the inequality correctly and solve it.

The total cost of the first phone after \( x \) months is given by: \[ 100 + 55x \] The total cost of the second phone after \( x \) months is given by: \[ 150 + 51x \]

We want to find when the second phone plan is less expensive than the first, which can be written as: \[ 150 + 51x < 100 + 55x \]

Now, we can reorganize the inequality to solve for \( x \):

1. Subtract \( 51x \) from both sides: \[ 150 < 100 + 4x \]

2. Subtract \( 100 \) from both sides: \[ 50 < 4x \]

3. Divide by \( 4 \): \[ 12.5 < x \]

This means that \( x > 12.5 \). Since \( x \) represents the number of months, it must be a whole number, so we round up to the next month. Therefore, 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.