Solving a percent mixture problem using a system of linear equations

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 20%

pure fruit juice, and the second type is 70%

pure fruit juice. The company is attempting to produce a fruit drink that contains 55%

pure fruit juice. How many pints of each of the two existing types of drink must be used to make 70

pints of a mixture that is 55%

pure fruit juice?

Answer 1

a + b = 70

0.2a + 0.7b = 0.55(70)

a = 70 - b

0.2(70 - b) + 0.7b = 38.5

14 - 0.2b + 0.7b = 38.5

0.5b = 24.5

b = 49 pints

a = 70 - 49

a = 21 pints