work problem with inequalities...

[Linxzie]

Err. Hi first of all. I am very confuzed at finding the inequalities in this problem. Don't know why. Here's the problem:

Ethel baby-sits for $4 per hour. She also works as a toutor for $7 per hour. Because of school, her parents only let her work for 12 hours per week. How many hours can Ethel tutor and baby-sit and still make at leat $50 per week?

Write a system of inequalities for this situation.

Please help..

 

[soroban]

Hello, Linxzie!

Ethel baby-sits for $4 per hour. She also works as a tutor for $7 per hour.
Because of school, her parents only let her work for 12 hours per week.
How many hours can Ethel tutor and baby-sit and still make at leat $50 per week?
Write a system of inequalities for this situation.

Let \(\displaystyle T\) = number of hours Ethel tutors per week: \(\displaystyle \,T\,\geq\,0\).
\(\displaystyle \;\;\) At $7/hour, she will make \(\displaystyle 7T\) dollars per week.

Let \(\displaystyle B\) = number of hours Ethel baby-sits: \(\displaystyle \,B\,\geq\,0\).
\(\displaystyle \;\;\)At $4/hour, she will make \(\displaystyle 4B\) dollars per week.

Her total income would be: \(\displaystyle 7T\,+\,4B\) dollars per week.

She wants this total to be at least $50: \(\displaystyle \,7T\,+\,4B\:\geq\:50\)

And her parents restrict her to a total of 12 hours per week: \(\displaystyle \,T\,+\,B\:\leq\:12\)

The inequalties are: \(\displaystyle \;\begin{array}{cccc}T\,\geq\,0 \\ B\,\geq\,0 \\ 7T\,+\,4B\:\geq\:50 \\ T \,+\,B\:\leq\:12\end{array}\)