math question?

Question

mom made two batches of iced tea. the first contained 6 percent sugar and was too sweet. the 2nd contained 3 percent sugar and was not sweet enough. how many cups should she take from each batch to make 9 cups of iced tea containing 4 percent sugar?

Answer 1

Let x be the amount of 6% sugar tea, and y be the amount of 3% sugar tea.

You want 9 cups total, so the sum of the amount of 6% and and the amount of 3% must be 9:

x + y = 9

And since the final batch is supposed to have 9 cups x 4% = 9(0.04) = 0.36 cups of sugar, and the first batch contributes x cups x 6% = 0.06x, and the second batch contributes y cups x 3% = 0.03y....

0.06x + 0.03y = 0.36

Or to get rid of the decimals, multiply through by 100:

6x + 3y = 36
x + y = 9

Those are your two equations. You can solve them any number of ways, but I'll pick substitution:

x = 9 - y
6(9 - y) + 3y = 36
54 - 6y + 3y = 36
-3y = -18
y = 6
x = 9 - y = 9 - 6 = 3

So she'd use 3 cups of the 6% tea and 6 cups of the 3% tea to get 9 cups of 4% tea.

Answer 2

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Answer 3

Solve the system of equation:

.06x+.03y=.04(9) (percent * amount)
x+y=9 (together you have 9 cups)

x=9-y substitute into 1st equation:

.06(9-y) +.03y = .36
.54-.06y+.03y=.36
-.03y=-.18
y=6 and x=3