Paige and Brooke make ice tea. Paige makes 18 ounces of iced tea that is 7% sugar. Brooke makes 10 ounce of iced tea that is 1% of sugar. They want to combine their tea to have 12 ounces of iced tea that is 3% sugar. How many ounces will Brooke have to contribute?
amount of Brooke's juice --- x ounces
amount of Paige's juice ---- 12-x ounces
.01x + .07(12-x) = .03(12)
times 100
x + 7(12-x) = 3(12)
x + 84 - 7x = 36
-6x = -48
x = 8
state your conclusion
p + b = 12 ... p = 12 - b
(p * .07) + (b * .01) = 12 * .03
substituting ... [(12 - b) * .07] + (b * .01) = 12 * .03
solve for b
To solve this problem, we need to set up an equation based on the given information.
Let's assume that Brooke will contribute x ounces of iced tea. Since we want to combine their teas to have 12 ounces of iced tea, this means Paige will contribute (12 - x) ounces of tea.
Now let's calculate the total sugar content in their combined tea. To do this, we can multiply the volume of each tea by its respective sugar percentage, add them together, and then divide by the total volume.
For Paige's tea:
Sugar content = 18 ounces * 7% = 1.26 ounces of sugar
For Brooke's tea:
Sugar content = x ounces * 1% = 0.01x ounces of sugar
The total sugar content in the combined tea:
Total sugar content = (1.26 + 0.01x) ounces
Now, we need to set up an equation based on the total sugar content and the desired sugar percentage (3%).
Desired total sugar content = Total volume * Desired sugar percentage
0.03 * 12 = (1.26 + 0.01x)
Now we can solve this equation to find the value of x, which represents the amount of tea Brooke needs to contribute.
0.36 = 1.26 + 0.01x (by multiplying 0.03 and 12)
0.01x = 0.36 - 1.26
0.01x = -0.9
x = -0.9 / 0.01
x = 90
According to our calculations, Brooke would need to contribute 90 ounces of iced tea to achieve the desired sugar percentage of 3% in their combined tea. However, since Brooke initially only has 10 ounces of tea, it is not possible to achieve the desired sugar content with the given quantities.