A hair company makes three batches of scented shampoo using the recipe shown. Each batch contains a different total amount of shampoo. 1/2 is pineapple, 1/5 is banana, 3/10 is coconut.

Batch 1:

Pineapple

Banana

Coconut is 2 1/10

Batch 2:

Pineapple

Banana is 3 1/5

Coconut

Batch 3:

Pineapple is 2 1/2

Banana

Coconut

Batch 1: Pineapple = 3 1/2 units, Banana = 1 2/5 units, Coconut = 2 1/10 units.

Batch 2: Pineapple = 8 units, Banana = 3 1/5 units, Coconut = 4 4/5 units.

Batch 3: Pineapple = 2 1/2 units, Banana = 1 unit, Coconut = 1 1/2 units.

We can represent pineapple as 1/2x, banana as 1/5x, and coconut as 3/10x. For batch 1, we have:

3/10x = 2 1/10

Write the mixed number as an improper fraction:

3/10x = 21/10

Divide both sides by 3/10:

3/10x : 3/10 = 21/10 : 3/10

x = 21/10 * 10/3 = 21/3 = 7

There are 7 total units in the shampoo. 2 1/10 are coconut; 1/2 (7) = 3 1/2 are pineapple; and 1/5 (7) = 1 2/5 are coconut.

For batch two, we have:

1/5x = 3 1/5

Convert to an improper fraction:

1/5x = 16/5

Divide by 1/5:

1/5x : 1/5 = 16/5 : 1/5

x = 16/5 * 5/1 = 16/1 = 16

There are 16 total units in the shampoo; 3 1/5 units of banana; 1/2 (16) = 8 units of pineapple; and 3/10 (16) = 4 4/5 units of coconut.

For batch 3:

1/2x = 2 1/2

Convert to improper fraction:

1/2x = 5/2

Divide by 1/2:

1/2x:1/2 = 5/2:1/2

x = 5/2*2/1 = 5/1 = 5

There are 5 total units in the shampoo; 2 1/2 units of pineapple; 1/5 (5) = 1 unit of banana; and 3/10 (5) = 1 1/2 units of coconut.