lines, functions, systems

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 45%

 pure fruit juice, and the second type is 100%

 pure fruit juice. The company is attempting to produce a fruit drink that contains 80%

 pure fruit juice. How many pints of each of the two existing types of drink must be used to make 110

 pints of a mixture that is 80%

 pure fruit juice?

Note that the ALEKS graphing calculator can be used to make computations easier.

Answer 1

45% and 100% to get 110 pints of 80%

100-80= 20

80-45 = 35

35/20 = 7/4 = 1.75 means 1.75 times as much pure 100% needed as 45%

7/4 = 70/40 = 70 pints 100% and 40 pints 45%

or try the conventional/traditional algebraic approach

.x + .45(110-x) = .8(110)

x -.45x = (.8-.45)110 = .35(110)

.55x = .35(110)

divide by 5

.11x = .07(110)

divide by 11

.01x = .07(10)

multiply by 100

x = 70 pints of purest juice ever

110-x = 40 pints of 45% juice

check the answers

.45(40) + 1.00(70) = 18 + 70 = 88 = .80(110) =88 It works