Question

A cosmetic company makes scented lotion using the recipe shown. Each bottle holds a different amount of lotion, in ounces. Drag numbers to show how much of each scent should be used in each bottle of lotion.

1/8 of the scent vanilla
3/8 of the scent almond
1/2 of the scent pineapple

Answer 1

Bottle 1: Vanilla - 1 ounce; Almond - 3 ounces

Bottle 2: Vanilla - 2 ounces; Pineapple - 8 ounces

Bottle 3: Almond - 4 1/2 ounces; Pineapple - 6 ounces

Explanation:

In Bottle 1, we are given the amount of pineapple. There are 4 ounces of pineapple in the lotion. Pineapple is 1/2 of the total amount of lotion; this gives us the equation

1/2x = 4

Divide both sides by 1/2:

1/2x ÷ 1/2 = 4 ÷ 1/2

x = 4/1 ÷ 1/2

To divide fractions, flip the second fraction and multiply:

x = 4/1 × 2/1 = 8/1 = 8

There are 8 total ounces of lotion.

1/8 of the lotion is vanilla:

1/8(8) = 8/8 = 1 ounce

3/8 of the lotion is almond:

3/8(8) = 24/8 = 3 ounces

In Bottle 2, we are given that there are 6 ounces of almond in the bottle. Almond is 3/8 of the total:

3/8x = 6

Divide both sides by 3/8:

3/8x ÷ 3/8 = 6 ÷ 3/8

x = 6/1 ÷ 3/8

Flip the second fraction and multiply:

x = 6/1 × 8/3 = 48/3 = 16 ounces

There are 16 ounces of lotion.

1/8 of the lotion is vanilla:

1/8(16) = 16/8 = 2 ounces

1/2 of the lotion is pineapple:

1/2(16) = 16/2 = 8 ounces

For Bottle 3, we are given that there are 1 1/2 ounces of vanilla. Vanilla is 1/8 of the total amount of lotion:

1/8x = 1 1/2

Convert the second fraction to an improper fraction:

1/8x = 3/2

Divide both sides by 1/8:

1/8x ÷ 1/8 = 3/2 ÷ 1/8

x = 3/2 ÷ 1/8

Flip the second fraction and multiply:

x = 3/2 × 8/1 = 24/2 = 12 ounces

There are 12 ounces of lotion.

3/8 of that is almond:

3/8(12) = 36/8 = 18/4 = 9/2 = 4 1/2 ounces

1/2 of the lotion is pineapple:

1/2(12) = 12/2 = 6 ounces

Answer 2

1/8 vanilla, 3/8 almonds, 1/2 pineapple.....ratio : 1/8,3/8,1/2

bottle 1 bottle 2 bottle 3

vanilla : 1 2 1 1/2

almond : 3 6 4 1/2

pineapple : 4 8 6