Question

The royal fruit company produces two types of of fruit drinks. The first type is 45% pure fruit juice and the second is 65% 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 drinks must be used to make 180 pints of a mixture that is 60% pure fruit juice.

Answer 1

Ah, I always enjoy mixture problems. The trick here is that you want to find the total amount of the pure fruit juice in each solution.

Drink A is 45% pure fruit juice, so 1 unit of drink A contains 0.45 units of fruit juice.
Drink B is 65% pure fruit juice, so 1 unit of drink B contains 0.65 units of fruit juice.

We know that we want to make 180 pints of 60% pure fruit juice.

We will use A for the number of pints of drink A, and B for the number of pints of drink B.

A + B = 180 (total we want to produce)
0.45A + 0.65B = 0.6(A+B) (final drink is 60% juice, so components must sum to that)

Now we solve the two equations by combination or substitution (given that the first equation is easily rearranged to give either A or B in terms of the other, I'd go with substitution).