posted by Gaby .
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?
I will do one of them in a systematic way, you then should be able to reason out the others without any actual work
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?
A=2/5 & 3/5
B=5/14 & 9/14
C=1/3 & 2/3