Answer:
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
