Amy must add 11 kg of peanuts to make a mixture with 80% peanuts
Step-by-step explanation:
The given is:
We need to find how many kg of peanuts she will add
Assume that Amy will add x kg of peanuts
∵ Amy has 4 kg of the mixed nuts
∵ She will add x kg of peanuts
∴ She will have 4 + x kg of the mixed nuts
∵ The quantity of 4 kg of mixed nuts containing 25% peanuts
∴ The quantity of peanuts in it = 25% × 4
∴ The quantity of peanuts in it = [tex]\frac{25}{100}[/tex] × 4 = 1 kg
∵ Amy will add x kg peanuts
∴ The quantity of the peanuts = 1 + x
∵ The quantity of peanuts in 4 + x kg of mixed nuts containing
80% peanuts
∵ 80% = 80 ÷ 100 = 0.8
- Equate the ratio between peanuts and the mixed nuts by 0.8
∴ [tex]\frac{1+x}{4+x}=0.8[/tex]
- By using cross multiplication
∴ 0.8 × (4 + x) = 1 + x
- Simplify the left hand side
∴ 3.2 + 0.8x = 1 + x
- Subtract 0.8x from both sides
∴ 3.2 = 1 + 0.2x
- Subtract 1 from both sides
∴ 2.2 = 0.2x
- Divide both sides by 2.2
∴ x = 11
To check your answer find the percentage of the peanuts in the mixture
∵ The quantity of the peanuts = 1 + 11 = 12 kg
∵ The quantity of the mixture = 4 + 11 = 15 kg
∵ [tex]\frac{12}{15}=0.8[/tex]
∵ 0.8 × 100% = 80%
∴ The answer is right
Amy must add 11 kg of peanuts to make a mixture with 80% peanuts
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