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 pure fruit juice?

Answer 1

• 55 pints of the 80% and 165 pints of the 100%

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Combine the two types of fruit drinks in the right proportions.

Let's use x pints for the 80% pure fruit juice and y pints for the 100% pure fruit juice.

We have two equations:

• 1) x + y = 220
• 2) 0.80x + 1.00y = 0.95 * 220

From equation 1, we can write

• y = 220 - x

Now substitute this expression for y in equation 2:

• 0.80x + 1.00(220 - x) = 209

Solve for x:

• 0.80x + 220 - x = 209
• 0.20x = -11
• x = 55

Now substitute x back into the expression for y:

• y = 220 - 55
• y = 165

The Royal Fruit Company must use 55 pints of the 80% and 165 pints of the 100% pure fruit juice drink.