For this exercise we can write and graph a system of inequalities. The system will have three inequalities.

Inequality (I) represents the total amount spent on savings and housing.
Inequality (II) represents the amount spent on savings.
Inequality (III) represents the amount spent on housing.

For all three inequalities, we will let $x$ represent the amount spent on savings and $y$ represent the amount spent on housing. It is given that the total amount earned in one paycheck is $2000$ dollars.

Writing the Inequalities

Inequality (I): It is given that we plan to spend less than half of one paycheck on savings and checking. Thus, we can write an inequality to represent this situation as the following way.

x + y < \frac{1}{2} \cdot 2000 \Rightarrow x + y < 1000

Inequality (II): It is given that we want to spend at least

10 %

of the paycheck on savings. The phrase at least can be interpreted as greater than or equal to and represented with

\geq .

Also, we can express

10 %

as

0.10 .

Then, we have the following inequality.

x \geq 0.10 \cdot 2000 \Rightarrow x \geq 200

Inequality (III): It is given that we want to spend at most

30 %

of the paycheck on housing. The phrase at most can be interpreted as less than or equal to and be represented with

\leq .

Also, we can express

30 %

as

0.30 .

Then we can write the following equality.

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