Question

The royal fruit company produces two type of fruit drinks. The first type is 70% pure fruit juice , and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 80% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 110 pints of a mixture that is 80% pure fruit juice

Answer 1

66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.

Explanation:

Let

x ----> pints of pure fruit juice at 70%

y ----> pints of pure fruit juice at 95%

we know that

`x+y=110` ---->
`x=110-y` ----> equation A

Remember that

`70\%=70/100=0.70`

`95\%=95/100=0.95`

`80\%=80/100=0.80`

so

`0.70x+0.95y=0.80(110)` ----> equation B

Solve the system by substitution

substitute equation A in equation B

`0.70(110-y)+0.95y=0.80(110)`

solve for y

`77-0.70y+0.95y=88`

`0.25y=88-77`

`0.25y=11`

`y=44`

Find the value of x

`x=110-y` --->
`x=110-44=66`

therefore

66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.