Four cups of pure water are added to a 20-cup bowl of punch that is 75% juice. What percentage of the new punch is juice?

Question

Original
Added
New
Amount of Juice
15 cups
0

Amount of Punch
20 cups
4 cups

27%
37.5%
62.5%
75%

Answer 1

In mixture problem, it's better to look at the actual volume first.

 

For example 4 cups of water plus 20 cups of juice is equal to 24 cups. Easy right?

 

4 + 20 = 24  equation 1.

 

Next, you will stick with the equation above but now, you will multiply their respective concentration.

 

The 20 cups of juice is mentioned as 75% juice. And the four cups of pure water is of course 0% juice.

 

Why settle with 0% juice for the water and not 100% PURE water? Because that's what the question needs, the %juice in the new mixture, and not %water.

 

From equation 1, we will just place the concentration beside its respective amount, let x be the new concentration:

 

4(0) + 20(.75) = 24(x)

 

0 + 15 = 24x

 

x = 15/24 = .625 = 62.5%