29.Paige and Brooke make iced tea. Paige makes 18 ounces of iced tea that is 7% sugar. Brooke makes 10 ounces of iced tea that is 1% sugar. They wanted to combine their tea to have 12 ounces of iced tea that is 3% sugar. How many sugar. How many ounces will Brooke have to contribute
A.4 ounces
B.6 ounces
C.8 ounces
D.10 ounces
I was wondering if Brooke would have to contribute 4 ounces. If not please explain the right answer.
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To find out how many ounces Brooke will have to contribute, we need to set up an equation based on the given information.
Let Brooke contribute x ounces of iced tea. Since the final mixture is 12 ounces, Paige will contribute (12 - x) ounces of iced tea.
The amount of sugar in Brooke's tea is given by:
(1/100) * 10 = 0.1 ounces of sugar.
The amount of sugar in Paige's tea is given by:
(7/100) * (12 - x) = (0.07) * (12 - x) = 0.84 - 0.07x ounces of sugar.
The amount of sugar in the final mixture is given by:
(3/100) * 12 = 0.36 ounces of sugar.
As we want the final mixture to have 0.36 ounces of sugar, the sum of sugar from Brooke's tea and Paige's tea must equal 0.36 ounces:
0.1 + 0.84 - 0.07x = 0.36.
Combining like terms, we get:
0.94 - 0.07x = 0.36.
Subtracting 0.94 from both sides, we have:
-0.07x = -0.58.
Dividing both sides by -0.07, we get:
x = 8.29.
Since we can't have a fractional amount of ounces, we round x to the nearest whole number, which is 8.
Therefore, Brooke will have to contribute 8 ounces of iced tea. The correct answer is option C, 8 ounces.