can you help me please with Math Word Problem.

Question

A bottle contains 900 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?

Answer 1

Look at the concentrations of actual fruit juice.

We start with 50% of 900 ml = 0.5(900) ml of juice

We subtract 100 ml of 50% juice or 0.5(100) ml

We then add back 100 ml of x% juice

Our total of actual juice is 48% of 900 ml or 0.48(900)

 

In equation we have:

0.5(900) - 0.5(100) + x(100) = 0.48(900)

450 - 50 + 100x = 432

400 + 100x = 432

100x = 32

x = 32/100 = 0.32

 

The added concentration was 32% juice