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Milk and cream contain different percents of butterfat. How much
2% milk needs to be mixed with how much
35% cream to give 20 L of
15% cream.

Milk and cream contain different percents of butterfat. How much $2 \%$ milk needs to be mixed with how much $35 \%$ cream to give $20$ L of $15 \%$ cream.

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Weighted averages: word problems

Full solution

Q. Milk and cream contain different percents of butterfat. How much

2 \%

milk needs to be mixed with how much

35 \%

cream to give

20

L of

15 \%

cream.

Set up equations: Set up the equation based on the percentages of butterfat in each component. $\newline$ Let $x$ be the amount of $2\%$ milk and $y$ be the amount of $35\%$ cream. $\newline$ We know that the total volume should be $20$ liters, so: $\newline$ $x + y = 20$
Second equation: Set up the second equation based on the butterfat content. $\newline$ The total butterfat from the milk and cream should equal the butterfat in the final mixture: $\newline$ $0.02x + 0.35y = 0.15 \times 20$
Simplify equation: Simplify the butterfat equation. $0.02x + 0.35y = 3$
Solve system: Solve the system of equations using substitution or elimination. $\newline$ From $x + y = 20$ , express $y$ in terms of $x$ : $\newline$ $y = 20 - x$ $\newline$ Substitute $y$ in the butterfat equation: $\newline$ $0.02x + 0.35(20 - x) = 3$
Substitute and solve: Distribute and combine like terms. $\newline$ $0.02x + 7 - 0.35x = 3$ $\newline$ $-0.33x + 7 = 3$
Combine terms: Solve for $x$ . $-0.33x = 3 - 7$ $-0.33x = -4$ $x = \frac{-4}{-0.33}$ $x = 12.12$
Find $x$ : Find $y$ using the value of $x$ . $y = 20 - 12.12$ $y = 7.88$

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