How many ounces of water must be added to 125oz of a 45% of sugar solution to produce a 30% sugar solution?

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A few days ago

MsMath

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Let x = the number of ounces of water.

You are given that 125 = the number of ounces of the 45% sugar solution.

The 30% sugar solution is a mixture of water and the 45% solution, so x+125 = the number of ounces of the 30% solution.

You have that x + 125 = x+125

Insert the percentages and solve.

x stands for water and water is 0% sugar, so put 0 in front of x.

125 is the 45% solution, so put .45 in front of 125

x+125 is the 30% solution, so put .30 in front of x+125

0*x + .45*125 = .30*(x+125)

Solve for x.

0 + 56.25 = .30x + 37.5

Subtract 37.5 from each side

18.75 = .30x

Divide both sides by .30

x = 62.5 ounces of water

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