Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 60% pure fruit juice, and the second type is 85% pure fruit juice. The company is

attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 160

pints of a mixture that is 70% pure fruit juice?

Answer 1

Answer: 96 pints of the first fruit drink (60% pure fruit juice) and 64 pints of the second fruit drink (85% pure fruit juice).

Step-by-step explanation:

This question is a system of equations. First, we will define our variables:

Let x= number of pints of the first fruit drink (60% pure fruit juice), and then y = the number of pints of the second fruit drink(85% pure fruit juice).

We know that there are 160 total pints of the mixture. Therefore,

x + y = 160 .......... equation i

We are also aware that 70% of those 160 pints will be pure fruit juice, and they will come from either x or y.

For x pints of the first juice, there is

0.6x of pure fruit juice and for y pints of first juice, there is 0.85y of pure fruit juice. Therefore, we will have:

0.6x + 0.85y = 160 × 0.7

0.6x + 0.85y = 112

Multiply through by 100 to remove decimal. This will be:

60x + 85y = 11200 ........... equation ii

Combine both equations

x + y = 160 .......... i

60x + 85y = 11200 ........ ii

Multiply equation i by 60

Multiply equation ii by 1

60x + 60y = 9600 ........ iii

60x + 85y = 11200 ......... iv

Subtract iv from iii

-25y = -1600

y = 1600/25

y = 64

Since x + y = 160

x = 160 - 64

x = 96

Therefore , we will need 96 pints of the first fruit drink (60% pure fruit juice) and 64 pints of the second fruit drink (85% pure fruit juice).