Question

Lenny makes $55,000 and is getting a $2,500 raise per year. Karl makes $62000, with a $2,000 raise per year. Which inequality shows how many years, y, will it take for Lenny to earn more than or the same salary as Karl. 55000x + 2500 ≤ 62000x + 2000 55000 + 2500x < 62000 + 2000x 55000 + 2500x ≤ 62000 + 2000x 55000 + 2500x ≥ 62000 + 2000x

Answer 1

`55000 + 2500x \geq 62000 + 2000x`

Explanation:

Given

Lenny:

Base Earnings = $55000

Raise = 2500 yearly

Karl:

Base Earnings = $62000

Raise = 2000 yearly

Required

Determine the inequality that takes years for Lenny to earn more or exact as Karl

Let y represent years:

Earnings = Base Earnings + Raise * Years

First, we need to determine Lenny's earning:

`Lenny: 55000 + 2500 * x`

`Lenny: 55000 + 2500x`

Next, we determine Karl's earning

`Karl: 62000 + 2000 * x`

`Karl: 62000 + 2000x`

To determine the required inequality, we have:

`Lenny \geq Karl`

This gives:

`55000 + 2500x \geq 62000 + 2000x`