Solving a percentage mixture

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is
80%
pure fruit juice, and the second type is
100%
pure fruit juice. The company is attempting to produce a fruit drink that contains
95%
pure fruit juice. How many pints of each of the two existing types of drink must be used to make
220
pints of a mixture that is
95%
pure fruit juice?

Answer 1

Let x = number of pints of 80% fruit juice

Let y =  number of pints of 100% fruit juice

x + y = 220     y = 220 - x

.8x + 1y = .95(220)

.8x + 220 - x = 209

-.2x = -11

x = 5.5 pints

y = 220 - 5.5 = 214.5 pints

 

 

Answer 2

(x pints)(80%) + (220 - x pints)(100%) = (220 pints)(95%)

80x + 22000 - 100x = 20,900

-20x = -1100

x = 55 pints of 80%

165 pints of 100%

Answer 3

Solve this system

x+y=220

0.8x+y=0.95*220

and get

x=55, y=165.