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.