SOLUTION: a bottle contains 750 ml of fruit punch with a concentration of 50% pure fruit juice. Jill drinks 100 ml of the punch and then refills the bottle with an equal amount of a cheaper

Question 149352: a bottle contains 750 ml of fruit punch with a concentration of 50% pure fruit juice. Jill drinks 100 ml of the punch and then refills the bottle with an equal amount of a cheaper brand of punch. If the concentration of juice in the bottle is now reduced to 48%, what was the concentration in the punch that jill added?
and the answer is 35% but how did they got the answer?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
a bottle contains 750 ml of fruit punch with a concentration of 50% pure fruit juice. Jill drinks 100 ml of the punch and then refills the bottle with an equal amount of a cheaper brand of punch. If the concentration of juice in the bottle is now reduced to 48%, what was the concentration in the punch that jill added?
.
Originally the bottle contained:
"750 ml of fruit punch with a concentration of 50% pure fruit juice"
.
Then, Jill drinks 100 ml of the punch:
Now, the volume is 750-100 = 650 ml
The amount of fruit juice is now: .50*650 = 325 ml
.
Then, Jill refills (100 ml) it with a "cheaper" brand bringing the total concentration to 48% fruit juice.
Let x = concentration of cheaper brand of punch
then
"amt of fruit juice from cheaper brand" + "amt of juice before refill" = "48% concentration"
.
This translates to:
100x + 325 = .48(750)
100x + 325 = 360
100x = 35
x = .35
.
Therefore, the concentration was 35%

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