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Katlin wants to make 64 ounces of chocolate milk that is 12% chocolate. She has light chocolate milk that is 5% chocolate and heavy chocolate milk that is 21% chocolate. How many ounces of light chocolate milk and heavy chocolate milk does Katlin need to combine? Choose 1 answer: (A) 24 light and 40 heavy (B) 28 light and 36 heavy (c) 36 light and 28 heavy (D) 40 light and 24 heavy

Katlin wants to make 6464 ounces of chocolate milk that is 12% 12 \% chocolate. She has light chocolate milk that is 5% 5 \% chocolate and heavy chocolate milk that is 21% 21 \% chocolate. How many ounces of light chocolate milk and heavy chocolate milk does Katlin need to combine?\newlineChoose 11 answer:\newline(A) 2424 light and 4040 heavy\newline(B) 2828 light and 3636 heavy\newline(C) 3636 light and 2828 heavy\newline(D) 4040 light and 2424 heavy

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Q. Katlin wants to make 6464 ounces of chocolate milk that is 12% 12 \% chocolate. She has light chocolate milk that is 5% 5 \% chocolate and heavy chocolate milk that is 21% 21 \% chocolate. How many ounces of light chocolate milk and heavy chocolate milk does Katlin need to combine?\newlineChoose 11 answer:\newline(A) 2424 light and 4040 heavy\newline(B) 2828 light and 3636 heavy\newline(C) 3636 light and 2828 heavy\newline(D) 4040 light and 2424 heavy
  1. Set up Equations: Let xx be the amount of light chocolate milk, and yy be the amount of heavy chocolate milk. We have two conditions:\newline11. The total amount of chocolate milk should be 6464 ounces.\newline22. The mixture should be 12%12\% chocolate.\newlineWe can set up two equations based on these conditions.
  2. First Equation: The first equation comes from the total amount of chocolate milk: x+y=64x + y = 64 This equation represents that the sum of light and heavy chocolate milk should equal 6464 ounces.
  3. Second Equation: The second equation comes from the percentage of chocolate in the mixture:\newline0.05x+0.21y=0.12×640.05x + 0.21y = 0.12 \times 64\newlineThis equation represents that the amount of chocolate from the light and heavy chocolate milk should equal 12%12\% of the total 6464 ounces.
  4. Solve for Total Chocolate Content: Now we solve the second equation for the total chocolate content:\newline0.05x+0.21y=0.12×640.05x + 0.21y = 0.12 \times 64\newline0.05x+0.21y=7.680.05x + 0.21y = 7.68\newlineThis equation will help us find the correct proportion of light and heavy chocolate milk to get the desired chocolate percentage.
  5. Express yy in terms of xx: We can use the first equation to express yy in terms of xx:y=64−xy = 64 - xNow we have yy in terms of xx, which we can substitute into the second equation to solve for xx.
  6. Substitute yy into Second Equation: Substitute y=64−xy = 64 - x into the second equation:\newline0.05x+0.21(64−x)=7.680.05x + 0.21(64 - x) = 7.68\newlineNow we will distribute the 0.210.21 into the parentheses and solve for xx.
  7. Distribute and Combine Terms: Distribute and combine like terms: \newline0.05x+13.44−0.21x=7.680.05x + 13.44 - 0.21x = 7.68\newline−0.16x+13.44=7.68-0.16x + 13.44 = 7.68\newlineNow we will subtract 13.4413.44 from both sides to isolate the term with xx.
  8. Isolate x Term: Subtract 13.4413.44 from both sides:\newline−0.16x=7.68−13.44-0.16x = 7.68 - 13.44\newline−0.16x=−5.76-0.16x = -5.76\newlineNow we will divide by −0.16-0.16 to solve for x.
  9. Solve for xx: Divide by −0.16-0.16:
    x=−5.76−0.16x = \frac{-5.76}{-0.16}
    x=36x = 36
    We have found that Katlin needs 3636 ounces of light chocolate milk.
  10. Find yy: Now we can find yy by substituting xx back into y=64−xy = 64 - x:
    y=64−36y = 64 - 36
    y=28y = 28
    Katlin needs 2828 ounces of heavy chocolate milk.

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