Sasha wants to make the most money she can while maintaining a 90 average. Currently she makes $9.00 per hour at her job. She knows she can maintain a 100 average if she does not work at all. She has observed that for every two hours of work, her average goes down by one point. How much money can she make each week while still maintaining a 90 average?
The correct answer and explanation is:
To solve this problem, let’s define the variables and create an equation based on the information provided.
- Sasha starts with a perfect average of 100, and for every two hours of work, her average decreases by one point.
- Sasha wants to maintain a 90 average, so her average should not fall below 90.
- She earns $9.00 per hour.
Step 1: Set up the equation for her average
Let xx represent the number of hours Sasha works per week. According to the problem, for every two hours of work, her average goes down by one point. This means that for xx hours of work, her average will decrease by x2\frac{x}{2} points.
Thus, Sasha’s average will be: Average=100−x2\text{Average} = 100 – \frac{x}{2}
Step 2: Set the condition for maintaining a 90 average
Sasha wants to maintain a 90 average, so we set the equation for her average to 90: 100−x2=90100 – \frac{x}{2} = 90
Step 3: Solve for xx
Now, solve for xx: 100−90=x2100 – 90 = \frac{x}{2} 10=x210 = \frac{x}{2}
Multiply both sides by 2: x=20x = 20
Step 4: Calculate how much Sasha can earn
Since Sasha can work for up to 20 hours per week without her average falling below 90, she can earn: Earnings=9×20=180\text{Earnings} = 9 \times 20 = 180
Conclusion:
Sasha can make $180 per week while maintaining a 90 average.