Question

You figured out that you could make $50 per pool to clean pools during the summer. You did, however, need to purchase some equipment to get started. After cleaning 3 pools you still were down a total of 15 dollars.

A) Write an equation to represents this situation
B) What is the y-intercept represent AND what does it represent?
C) How much money will you have made after cleaning 12 pools.

Answer 1

The equation to represent the situation is y = 50x - 165. The y-intercept of -165 represents the initial cost of equipment. After cleaning 12 pools, the earnings would be $435.

Step-by-step explanation:

Equation Development

To represent the situation where you make $50 per pool cleaned, but are still down $15 after cleaning 3 pools, you can set up the following equation:

Let y = total earnings after cleaning x pools.

The equation is: y = 50x - c, where c is the initial cost of the equipment. Because after cleaning 3 pools (x = 3) you are down $15 (y = -15), we can substitute these values into the equation to find c.

-15 = 50(3) - c

-15 = 150 - c

c = 150 + 15

c = 165

Thus, the equation representing the situation is: y = 50x - 165.

Y-intercept Interpretation

The y-intercept is -165, which represents the initial cost of the equipment needed to start the pool cleaning service. This is the amount you are down before cleaning any pools.

Earnings after Cleaning 12 Pools

To calculate how much money you will have made after cleaning 12 pools, substitute x = 12 into the equation:

y = 50(12) - 165

y = 600 - 165

y = 435

After cleaning 12 pools, you will have made $435.