2.10.2 Using Inequalities to Solve a Problem

Using Inequalities to Solve a Problem

Let’s look at an example where we might be able to solve a problem using inequalities.

A school is repainting its classroom walls. The school has at most 30 gallons of paint. The painter needs $\frac{5}{2}$ gallons of paint for each classroom. How many classrooms can the school paint at most?

We know that the answer is greater than or equal to 0 classrooms, so $x\ge 0$.

We also know that each classroom requires $\frac{5}{2}$ or 2.5 gallons of paint.

Let’s take a guess at how many classrooms and check if we are close to the solution. How many gallons of paint would we need to paint 10 classrooms?

$10\times 2.5=25$, and since $25<30$, it could be possible for the school to paint 10 classrooms.

We can try 11 classrooms.

$11\times 2.5=27.5$, and since $27.5<30$, it could be possible for the school to paint 11 classrooms.

We can try 12 classrooms.

$12\times 2.5=30$, and since $30=30$, the most classrooms the school could paint is 12 classrooms.