Question

To create a breakfast beverage, cherry juice in two concentrations, 19% and 60%, must be combined into a solution that will be mixed with another type of juice to produce the beverage. If 70 gallons of 19% juice is used, how many gallons of the 60% juice must be used to obtain a 50% cherry juice solution?

Answer 1

19% (70) + 60% (x) = 50% (x+70)
0.19(70) + 0.6x=0.5 (x+70)
13.3 + 0.6x=0.5x+35
0.6x-0.5x=35-13.3
Can you solve it for x now?

Answer 2

217?

Answer 3

Because 19% juice is used in 70 gallons and 60% juice is used in x gallons. Together they add up to make 50% of their sum i.e (70+x)

Answer 4

yup. you got it ;)

Answer 5

sweet

Answer 6

You are looking for the solution to this equation:

\[\frac{70 \times 0.19 + x \times 0.6}{70 + x} = 0.5\]

that is, the gallons of pure cherry juice, divided by the total gallons in the solution, must be equal to 50%, or 0.5

So we must solve for x, the number of gallons of the second solution.

70(0.19) + 0.6x = 0.5(70 + x)

13.3 + 0.6x = 35 +0.5x
0.1x = 35 - 13.3
x = 21.7 / 0.1
x = 217.

Therefore you must add 217 gallons of the 60% juice.


We can verify this:

70 gallons @ 19% = 13.3 gallons of cherry
217 gallons @ 60% = 130.2 gallons of cherry

143.5 gallons of cherry / 287 total gallons = 50% cherry