Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 85% 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 60 pints of a mixture that is 60% pure fruit juice?

Answer 1

Answer: We need we need 10 pints of the second fruit juice (85% pure fruit juice). Therefore, we need

(60-10 = 50) pints of the first fruit juice (55% pure fruit juice).

Explanation:

Let x be number of pints of the first fruit drink which is ( 55% pure fruit juice), while y will be the number of pints of second fruit drink (85% pure fruit juice).

We know that there are 60 total pints. Therefore:

x + y = 60

We also know that 60% of the 60 pints will be pure fruit juice, and the pure fruit juice will either come from

x or y.

For x pints of first juice, there is 0.55x pure fruit juice while for y pints of first juice, there is 0.85y pure fruit juice. Therefore, we get:

0.55x + 0.85y = 60 × 0.6

0.55x + 0.85y = 36

We will get rid of the decimals by multiplying through by 100. This will be:

55x + 85y = 3600

Combining both equations

x + y = 60 .......... i

55x + 85y = 3600 ........ ii

Multiply equation i by 55

Multiply equation ii by 1

55x + 55y = 3300

- 55x + 85y = 3600

Then subtract

-30y = -300

y = 10

Therefore, we need we need 10 pints of the second fruit juice (85% pure fruit juice). Therefore, we need

(60-10 = 50) pints of the first fruit juice (55% pure fruit juice).