Question

Yuri makes his own citrus vinaigrette salad dressing. He likes the dressing best if it contains 40% fruit juice. He has a bottle of dressing mixture that contains 60% juice and 3 cups of dressing that contains 20% juice. How much of the dressing mix with 60% juice should Yuri add to the dressing mix with 20% juice to get the dressing he prefers with 40% juice? Show your work.

Answer 1

ready?

Answer 2

how do you set it up? I know it's the (amount of mixture A)(% mixture A) + (amount of mixture B)(%mixtureB) = (amount resulting mixture)(%resulting mixture) but i don't understand what to put for each thing @satellite73

Answer 3

wth i don't know
lets to it like this
he has 3 cups that contain 20% fruit juice
how much fruit juice is in those 3 cups exactly?

Answer 4

3/20?

Answer 5

no

Answer 6

20% of 3 means \(.2\times 3=.6\)

Answer 7

so he currently has \(.6\) cups of fruit juice

Answer 8

ohhh

Answer 9

now lets introduce a variable, say \(x\) is the amount of 60% fruit juice
if he adds \(x\) cups of 60% fruit juice he will have
a) \(.6+.6x\) cups of fruit juice and
b) \(3+x\) cup of dressing all together

Answer 10

you want the amount of fruit juice to be 40% of the total, in other words \(.4(3+x)\)

Answer 11

let me know when i lost you
we are almost done

Answer 12

last job is to set
\[.6+.6x=.4(x+3)\] and solve for \(x\)
probably easier if you multiply both sides by 10 to get rid of the annoying decimals and write
\[6+6x=4(x+3)\]
can you solve that one?