Question

Adam plans a diet for his dog, Louie. Louie consumes between 510 and 540 calories per day. If Louie eats 1 1/2 servings of dog food each day, how many treats can Louie have?

Dog Food 320 Calories per serving
Treats 10 Calories per treat

Write and solve a compound inequality to represent this situation. Let x represent the number of treats Louie can have each day.

Answer 1

The compound inequality is
`510 \leq 10x+480 \leq 540`

`3 \leq x \leq 6`

Explanation:

Let

x -----> represent the number of treats Louie can have each day

step 1

Find the number of calories for 1 1/2 serving of dog

1 1/2=1.5

one serving is 320 calories

so

1.5*320=480 calories

step 2

Find the compound inequality

The compound inequality is

`510 \leq 10x+480 \leq 540`

Divide in two inequalities

`10x+480\geq 510` ------> inequality A

`10x\geq 510-480`

`10x\geq 30`

`x\geq 3\ treats`

`10x+480\leq 540` -----> inequality B

`10x\leq 540-480`

`10x\leq 60`

`x\leq 6\ treats`

therefore

The compound inequality is equal to

`3 \leq x \leq 6`