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
Q. 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
Define Variables: Let x be the amount of light chocolate milk, and y be the amount of heavy chocolate milk. We have two conditions:1. The total amount of chocolate milk should be 64 ounces: x+y=642. The mixture should be 12% chocolate: 0.05x+0.21y=0.12×64Now we will solve this system of equations.
Express y in terms of x: First, we will express y in terms of x from the first equation: y=64−x.
Substitute y in the second equation: Next, we substitute y in the second equation with 64−x:0.05x+0.21(64−x)=0.12×64
Distribute and simplify the equation: Now we will distribute and simplify the equation: 0.05x+13.44−0.21x=7.68
Combine like terms: Combine like terms: −0.16x+13.44=7.68
Isolate the term with x: Subtract 13.44 from both sides to isolate the term with x: −0.16x=7.68−13.44 −0.16x=−5.76
Solve for x: Divide both sides by −0.16 to solve for x:x=−0.16−5.76x=36
Find y: Now that we have the value for x, we can find y by substituting x back into the equation y=64−x: y=64−36 y=28
Final Solution: We have found that Katlin needs 36 ounces of light chocolate milk and 28 ounces of heavy chocolate milk to make the desired mixture.
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