# Math

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Mix A=2 cups concentrate:3 cups water
Mix B=5 cups concentrate:9 cups water
Mix C=1 cups concentrate:2 cups water
Mix D=3 cups concentrate:5 cups water

For each mix, how much concentrate and how much water are needed to make 1 cup of juice?

• Math -

I will do one of them in a systematic way, you then should be able to reason out the others without any actual work

MIX D
conentrate:water = 3:5

let the amount of concentrate be 3x
and the amount of water be 5x

(notice 3x:5x = 3:5)

then 3x + 5x = 1
8x = 1
x = 1/8
so concentrate = 3x = 3/8 of a cup
water = 5x = 5/8 of a cup

notice how 3/8 + 5/8 = 1
notice 3/8 : 5/8 = 3:5

can you now do the others by observing how the 8 was obtained?

• Math -

Thanks!!!
A=2/5 & 3/5
B=5/14 & 9/14
C=1/3 & 2/3

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