identify the problem and explain

Question

A student is working two jobs over the summer to pay for a new car. The student gets paid $25 for each lawn that is mowed and $15 for each pool that is cleaned . The student wants to earn $750 to pay for a down payment on a car. The equation that represents this relationship is .

1. Use the equation to identify the x-intercept.
2. Explain what the x-intercept means in the context of the problem. (write a sentence & use units)
3. Use the equation to identify the y-intercept.
4. Explain what y-intercept means in the context of the problem. (write a sentence & use units)
5. Use the equation to identify one other possible solution.
6. Explain what that solution means in the context of the problem. (write a sentence & use units)

Answer 1

Let x = the number of lawns mowed and let y = the number of pools cleaned.

25x + 15y = 750

Along the x-axis, y = 0, right?

25x + 15(0) = 750

25x = 750

x = 30

(30,0)

This means if no pools are cleaned, 30 lawns must be mowed.

Along the y-axis, x = 0.

25(0) + 15y = 750

15y = 750

y = 50

(0,50)

If no lawns are mowed, 50 pools must be cleaned.

Now, pick another number for either. What if x = 3?

25(3) + 15y = 750

75 + 15y = 750

15y = 675

y = 45

(3,45)

If 3 lawns are mowed, 45 pools must be cleaned.