Question

The Royal Fruit Company produces two types 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 120 pints of a mixture that is 80% pure fruit juice?

Answer 1

put the number of pints of 95% fruit juice as say \(x\) then since the total is 120 the number of pints of 70% juice is necessarily \(120-x\)
the total amount of fruit juice is therefore
\[.95x+.70(120-x)\] and since you want this to be 80% of 120 = 96 set
\[.95x+.70(120-x)=96\] and solve for \(x\)
probably easier to multiply by 100 to rid yourself of the annoying decimals and write
\[95x+70(120-x)=9600\]

Answer 2

so thats you find your first type how exactly would you change your equation to find the second type

Answer 3

you can either do this by hand, which is not that hard,
\[95x+8400-70x=9600\]
\[25x+8400=9600\]
\[25x=1200\]
\[x=1200\div 25=48\]so 48 pints of the 95% and therefore \(120-48=72\) pints of the 70%

Answer 4

i wouldn't change it at all.
if i know the amount of 95% juice i also know the amount of 70% juice because they have to total 120 pints

Answer 5

i got x=48 :)

Answer 6

on the other hand you could start with
\[.70x+.95(120-x)=96\] and get the amount of 70 juice
it makes no difference

Answer 7

so first answer 95% second 70% ?

Answer 8

or do i give the whole numbers as answers

Answer 9

nvm