How many ounces of dried apricots must be added?

Question

How many ounces of dried apricots must be added to 18 ounces of a snack mix that contains 20% dried apricots to make a mixture that is 25% dried apricots?

Answer 1

The fastest way to solve this is to not care about the percentage (concentration) first. Just look at the actual weight or volume that is being described.

 

18 (snack mix) + x (apricots that you don't know) = (18+x) (the new mixture)

 

18 + x = (18+x) ---> (duh right?)

 

Next, let's apply the concentration:

 

For the snack mix it's 20% apricots. 

 

For the apricots that you gonna add, it's pure apricot therefore 100%.

 

And the desired concentration for the new mix is 25% apricots.

 

Multiplying the concentrations to their corresponding magnitudes:

 

18*(0.2) + x*(1.0) = (18+x)*(0.25) ----------- (you can actually use 20, 100 and 25 if you want, doesn't matter)

 

3.6 + x = 4.5 + 0.25x

0.75x = 0.9

 

x = 1.2 ounces of apricots