Problema Solution
the royal fruit company produces two types of fruit drinks. the first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. the company is attempting to produce a fruit drink that contains 60% pure fruit juice. how many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 60% pure fruit juice?
Answer provided by our tutors
let
x = the pints of 55% pure fruit juice, x>0
y = the pints of 80% pure fruit juice, y>0
by mixing x and y we get total of 80 pints that is
x + y = 80
also
55% of x + 80% of y = 60% of 80
0.55x + 0.80y = 0.60*80
by solving the system of equations
x + y = 80
0.55x + 0.80y = 0.60*80
we find
x = 64 pints
y = 16 pints
64 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice should be used to make 80 pints of a mixture that is 60% pure fruit juice.