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Question

33) 1 fl. oz. of a sugar solution was mixed with 2 fl. oz. of a 38% sugar solution to make a 36% sugar solution. Find the percent concentration of the first solution.

Answer 1

The trick is to keep track of the ozs of sugar in the solutions.

2 oz. x 0.38 = 0.76 oz in the 2nd sol'n.

The resulting solution is 1 + 2 = 3 oz x .0.36 = 1.08 oz.

so there must have beed 1.08 - 0.76 = 0.32 oz in the unknown solution

0.32 oz sugar/1 oz sol'n = 32%

As an algebra solution it looks like 1x + 2(0.38) = 3(0.36)

x + 0.76 = 1.08

x = 0.32, or 32%

Check: 1(.32) = 0.32 oz sugar

2(0.36) = 0.76 oz sugar

1.08 oz sugar in 3 oz sol'n = 1.08/3 = 0.36 (36%)

Answer 2

Let x=concentration of 1st solution

The volume of the finished solution is 3 fl oz.

Then write volume *concentration as follows: 1*x + 2.38=3*.36

You take it from here.

Remember your answer for x will be a decimal fraction which will need to be multiplied by 100 to make %.