Question

new Question!

Answer 1

10.15]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 2

Does anyone understand this?

Answer 3

I do. What don't you understand?

Answer 4

The entire thing!

Answer 5

I know it is a mixture solution though. :(

Answer 6

What is your unknown here

Answer 7

The dressing mix he should add?

Answer 8

more specifically, it's the amount of the 60% solution

Answer 9

so let x = amount of the 60% solution

Answer 10

in cups

Answer 11

Ok, :) Then?

Answer 12

It literally says "3 cups of dressing that contains 20% juice"

so we know that there are a total of 3+x cups of salad dressing.

Answer 13

In those 3 cups of 20% juice, there are 3*0.2 = 0.6 cups of pure juice

Answer 14

Ok, is that it?

Answer 15

no, I'm walking you through it

Answer 16

Okay. :D

Answer 17

In the other x cups of 60% juice, there are 0.6x cups of pure juice

Answer 18

We want the total concentration of juice to be 40%, so this means that we want (3+x)*0.4 = 1.2+0.4x cups of pure juice at the end (when we're done mixing everything)

Answer 19

So this means

(Amount of Pure Juice from the 20% solution) + (Amount of Pure Juice from the 60% solution) = Amount of Pure Juice in the 40% final solution


which turns into


0.6 + 0.6x = 1.2+0.4x


Solve that for x to find your answer

Answer 20

Is it 2 cups?

Answer 21

no

Answer 22

Oh, okay...hmm. :(

Answer 23

Would it be a decimal answer?

Answer 24

no, it's a whole number

Answer 25

3 cups?

Answer 26

you got it

Answer 27

OPk, thx! :D

Answer 28

np