The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 60% pure fruit juice. The company is attempting to produce a fruit drink that contains 55% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 140 pints of a mixture that is 55% pure fruit juice?
Note that the ALEKS graphing calculator can be used to make computations easier.
Firstfruitdrink: pints Secondfruitdrink: pints

GIVEN: The Royal Fruit Company produces two types of fruit drinks. The first type is [tex]35\%[/tex] pure fruit juice, and the second type is [tex]60\%[/tex] pure fruit juice. The company is attempting to produce a fruit drink that contains [tex]55\%[/tex] pure fruit juice.

TO FIND: How many pints of each of the two existing types of drink must be used to make [tex]140[/tex] pints of a mixture that is [tex]55\%[/tex] pure fruit juice.

SOLUTION:

Let the quantity of first type of juice be [tex]x\text{ pints}[/tex]

Quantity of second type of juice [tex]=140-x\text{ pints}[/tex]

Concentration of pure juice in final mixture [tex]=55\%[/tex]

Now,

The concentration of pure juice in final mixture is sum of concentrations of pure juice in first and second type of juice

[tex]\frac{55}{100}\times140=\frac{35}{100}\times x + \frac{60}{100}\times (140-x)[/tex]

[tex]25x=700[/tex]

[tex]x=28[/tex]

Quantity of first type of juice [tex]=28\text{ pints}[/tex]

Quantity of second type of juice [tex]=140-28=112\text{ pints}[/tex]

Hence quantity of first and second type of juice is 28 pints and 112 pints respectively.