Question

6.) Mrs. Brown plans a diet for herself.

She consumes between 1600 and 1800
per day. She wants to eat a treat that is
10 calories each. She eats one meal a
day that is 1,000 calories a serving. If
she eats 0.5 a serving of food each day,
how many treats can she have in her
new calorie range? Write the
compound inequality and solve.

Answer 1

To find out how many treats Mrs. Brown can have in her calorie range, you can set up a compound inequality based on her daily calorie intake:

Let x be the number of treats.

Mrs. Brown consumes 1,000 calories for her meal and x treats, with each treat being 10 calories. Her total calorie consumption can be represented as:

1,000 (meal) + 10x (treats)

She wants her daily calorie consumption to be between 1600 and 1800 calories:

So, the compound inequality can be written as:

1600 ≤ 1,000 + 10x ≤ 1800

Now, solve this compound inequality:

Start with the left inequality:

1600 ≤ 1,000 + 10x

Subtract 1,000 from both sides to isolate 10x:

1600 - 1,000 ≤ 10x

600 ≤ 10x

Divide both sides by 10 to solve for x:

x ≥ 60

Now, let's move on to the right inequality:

1,000 + 10x ≤ 1800

Subtract 1,000 from both sides:

10x ≤ 800

Divide both sides by 10:

x ≤ 80

So, Mrs. Brown can have between 60 and 80 treats within her calorie range of 1600 to 1800 calories per day.