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

Answer:

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

$3 \leq x \leq 6$

Step-by-step 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

$3 \leq x \leq 6$