Question

1. Beatrice started babysitting when she was in high school. She has built a reputation for herself and has become popular among the neighborhood parents.

Beatrice charges $10/h and gets a $5 automatic tip. Beatrice needs $100 to buy a present for her mother. She wants to find out the minimum number of hours she needs to babysit at one job to get the money she needs.
(a) Write an inequality and solve it to help Beatrice figure out the minimum number of hours. Identify what the variable is and what it represents. Show your work. Justify each step in the solution.
(b) Graph the solution on a number line.
(c) Beatrice doesn’t charge for partial hours. What is the minimum number of hours that she needs to work at one job to make at least $100? Round your answer to the nearest hour. Justify your answer.

Answer 1

Part (a):
She charges $10 per hour and charges $5 automatic tip.
Assuming that she works x hours and makes a total of y dollars, the equation indicating the amount she makes (y) will be as follows:
y = 5 + 10x
Now, she needs $100 to buy the present. This means that the amount she makes (y) should be at least 100.
Therefore, the inequality will be as follows:
y ≤ 5 + 10x
we will substitute in the above inequality with y = 100 and solve for the number of hours (x) as follows:
y ≤ 5 + 10x
100 ≤ 5 + 10x
95 ≤ 10x
9.5 ≤ x
This means that she needs to babysit at least 9.5 hours to make the $100.

Part (b):
On the number line, we will take all numbers that are greater than on equal 9.5. Check the attachment.

Part (c):
If she doesn't charge for partial hours, then she would need to work 10 hours in order to make the $100 she wants.

We have calculated that she needs to work at least 9.5 hours to make the necessary money.
Assuming that we will round down. This means that she will work 9 hours. In this case, she will make:
y = 5 + 9(10) = $95 ...........> rejected
Assuming that we will round up. This means that she will work 10 hours. In this case, she will make:
y = 5 + 10(10) = $105 .........> accepted

Hope this helps :)