You earn money by babysitting for $8.00 per hour and by raking leaves for $7.00 per hour. You have 9 hours available for work. What is the greatest number of hours you can spend raking and still make ant least $68.00?

forgot to put the choices.

a. 3 hours
b. 4 hours
c. 5 hours
d. 6 hours

x+y <= 9

8x+7y <= 68
graph those regions and check the highest integer value of y that is in the shaded area.

To determine the number of hours you can spend raking and still make at least $68.00, we can set up an equation.

Let's say x is the number of hours you spend raking.

The amount of money earned by babysitting is 8 * (9 - x) since you have 9 hours available and will spend x hours raking.

The amount of money earned by raking is 7 * x.

The total amount earned by both activities is $68.00.

We can write the equation as:
8 * (9 - x) + 7 * x = 68

Simplifying the equation gives:
72 - 8x + 7x = 68
-1x = -4
x = 4

Therefore, the greatest number of hours you can spend raking and still make at least $68.00 is 4 hours.

To find the greatest number of hours you can spend raking leaves while still making at least $68.00, we need to set up a system of inequalities.

Let's assume you spend x hours raking leaves and (9 - x) hours babysitting.

The amount earned from raking leaves can be calculated by multiplying the hourly rate by the number of hours: 7x.

The amount earned from babysitting can be calculated by multiplying the hourly rate by the number of hours: 8(9 - x).

To find the greatest number of hours of raking, we need to find the maximum value of x that satisfies the inequality:

7x + 8(9 - x) ≥ 68

Let's solve for x:

7x + 72 - 8x ≥ 68
-x + 72 ≥ 68
-x ≥ -4

Multiply both sides by -1 (which reverses the inequality sign):

x ≤ 4

Therefore, the greatest number of hours you can spend raking leaves while still making at least $68.00 is 4 hours.