a fruit punch that contains 10% is combined with 100% fruit juice. how many ounces of each should be used to make 40oz of a mixture that is 55% fruit juice?

Question

applications of systems

Answer 1

You can solve this by setting up a weighted combination of the juices.

 

x = ounces of 10%

40 - x = ounces of 100%

 

(10%)x + (100%)(40 - x) = (55%)(40 oz)

 

10x + 100(40 - x) = 2200

 

Solve for x.

 

-90x = -1800

 

x = 1800/90 = 20 oz

 

40 - x = 40 - 20 = 20 oz

 

You need 20 oz of both.

Answer 2

We combine x ounces of 100% juice

with 40-x of 10% juice

to get 40 ounces of 55% juice

 

x + 0.1(40-x) = .55(40)

x + 4 - 0.1x = 22

0.9x + 4 = 22

.09x = 18

x = 20 ounces of 100% juice

40-x = 20 ounces of 10% juice

 

We combine 20 ounces of each.