Ahair 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; Banana = 1 2/5

Batch 2:  Pineapple = 8; Coconut = 4 4/5

Batch 3:  Banana = 1; Coconut = 1 1/2

Step-by-step explanation:

For Batch 1:

We know that coconut is 3/10 of the mixture, and we have 2 1/10 coconut:

3/10x = 2 1/10

Converting 2 1/10 to an improper fraction, we have

3/10x = 21/10

Divide both sides by 3/10:

3/10x ÷ 3/10 = 21/10 ÷ 3/10

To divide fractions, flip the second one and multiply:

x = 21/10 × 10/3 = 210/30 = 7

This means we have 7 total of the mixture.

1/2 of this is pineapple:  1/2(7) = 7/2 = 3 1/2

1/5 is banana:  1/5(7) = 7/5 = 1 2/5

For Batch 2:

1/5 of the total is banana; we have 3 1/5 banana:

1/5x = 3 1/5

Convert the second fraction to an improper fraction:

1/5x = 16/5

Divide both sides by 1/5:

1/5x÷1/5 = 16/5÷1/5

Flip the second fraction and multiply:

x = 16/5×5/1 = 80/5 = 16

We have 16 of the total shampoo.

Pineapple is 1/2 of this:

1/2(16) = 8

Coconut is 3/10 of the total:

3/10(16) = 48/10 = 4 8/10 = 4 4/5

For Batch 3:

Pineapple is 1/2 of the total.  We have 2 1/2 pineapple:

1/2x = 2 1/2

Convert the fraction on the right to improper:

1/2x = 5/2

Divide both sides by 1/2:

1/2x÷1/2 = 5/2÷1/2

Flip the second fraction and multiply:

x = 5/2×2/1 = 10/2 = 5

We have 5 total shampoo.

Banana is 1/5 of this:

1/5(5) = 1

Coconut is 3/10 of this:

3/10(5) = 15/10 = 1 5/10 = 1 1/2

step-by-step explanation:

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