Angela is renting a truck to move. The rental company charges $25 plus $10 per hour to rent the truck. Angela wants to spend no more than $75. What constraints apply to this situation? What is the maximum number of hours Angela can rent the truck?

Let M = the money spent on a moving truck.

The constraints on this problem are that 25 ≤ M ≤ 75. No matter how long the truck is used, she spends $25. The most she can spend is $75. To find out how long she can use it, let's change the variable. Her spending is $25 plus $10 for each hour. Let each hour be H, and her spending becomes 25 + 10H. Now we put that into the equation for M

25 ≤ 25 + 10H ≤ 75

Since we want the maximum amount, we focus on the $75.

25 + 10H ≤ 75

10H ≤ 50 subtract 25 on both sides

H ≤ 5

We want the maximum to make this true, so H = 5 (as 5 ≤ 5 is true)

Thus, our constraints are 25 ≤ M ≤ 75 and the most she can have the truck is for 5 hours.

She can have it for 5 hours