Algebra 2 question help

Question

Georgia has up to 30 hours a week to study for her math and history classes. She needs to study at least 12 hours a week to pass her math class. Write a system of inequalities to describe the possible amounts of time she can study for each subject.

Answer 1

This example requires us to set up two systems of inequalities. First, let's assign variables. Let's say that the number of hours she spends studying math is "m" and the number of hours she spends studying history is "h".

First, we know that the number of hours she spends studying both subjects together can be up to, not over, 30 hours, This means that when we add up "m" and "h", it needs to be less than or equal to 30, thus giving us our first inequality:

m + h ≤ 30

The second part tells us that the number of hours that she has to study math, "m", should be at least 12. This means "m" needs to be greater than or equal to 12:

m≥12

So our two inequalities will be:

m + h ≤ 30

m≥12

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