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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

Full solution

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. Define Variables: 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: x+y=64x + y = 64\newline22. The mixture should be 12%12\% chocolate: 0.05x+0.21y=0.12×640.05x + 0.21y = 0.12 \times 64\newlineNow we will solve this system of equations.
  2. Express yy in terms of xx: First, we will express yy in terms of xx from the first equation: y=64xy = 64 - x.
  3. Substitute yy in the second equation: Next, we substitute yy in the second equation with 64x64 - x:0.05x+0.21(64x)=0.12×640.05x + 0.21(64 - x) = 0.12 \times 64
  4. Distribute and simplify the equation: Now we will distribute and simplify the equation: 0.05x+13.440.21x=7.680.05x + 13.44 - 0.21x = 7.68
  5. Combine like terms: Combine like terms: \newline0.16x+13.44=7.68-0.16x + 13.44 = 7.68
  6. Isolate the term with xx: Subtract 13.4413.44 from both sides to isolate the term with xx:
    0.16x=7.6813.44-0.16x = 7.68 - 13.44
    0.16x=5.76-0.16x = -5.76
  7. Solve for x: Divide both sides by 0.16-0.16 to solve for x:\newlinex=5.760.16x = \frac{-5.76}{-0.16}\newlinex=36x = 36
  8. Find yy: Now that we have the value for xx, we can find yy by substituting xx back into the equation y=64xy = 64 - x:
    y=6436y = 64 - 36
    y=28y = 28
  9. Final Solution: We have found that Katlin needs 3636 ounces of light chocolate milk and 2828 ounces of heavy chocolate milk to make the desired mixture.

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