# Kaitlin knows that if she needs to add antifreeze to her car’s radiator the mixture used must contain 50% antifreeze and 50% water. How many gallons of a mixture containing 80% antifreeze must be added to a 3-gallon mixture containing 40% antifreeze to obtain the mixture Kaitlin needs?

Question
Ratios, rates, proportions
Kaitlin knows that if she needs to add antifreeze to her car’s radiator the mixture used must contain 50% antifreeze and 50% water. How many gallons of a mixture containing 80% antifreeze must be added to a 3-gallon mixture containing 40% antifreeze to obtain the mixture Kaitlin needs?

2021-02-22
Let x be the amount of 80% antifreeze to be added, in gallons.
In terms of percentage of antifreeze, we write:
40% of 3 gallons+80% of x gallons=50% of 3+x gallons
0.4(3)+0.8(x)=0.5(3+x)
Solve for x:
1.2+0.8x=1.5+0.5x
0.8x=0.3+0.5x
0.3x=0.3
x=1
So, Kaitlin needs to add 1 gallon of 80% antifreeze.

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