ratios

the following is re-posted from this thread.
the original thread contains sundry followup comments, so you may want to go have a look at them.

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the easiest way to do this is to pick numbers. in fact, you can pick numbers on ALL problems whose question prompts feature the words "in terms of", because such problems, by definition, work with any given values of those variables.

let's pick easy numbers: y = 2, z = 4. (these aren't totally random. the choice for y is essentially random, but z has been deliberately chosen so that #2 and #5 will be integers.)

then we have:
x gallons of 1% = 0.01x gallons of fat
2 gallons of 2% = 0.02(2) = 0.04 gallons of fat
4 gallons of 3% = 0.03(4) = 0.12 gallons of fat
total fat = 0.01x + 0.04 + 0.12 = (0.01x + 0.16) gallons
total volume = x + 2 + 4 = (x + 6) gallons

so:
(0.01x + 0.16)/(x + 6) = 0.015
multiply by 100 ----- (x + 16)/(x + 6) = 1.5
multiply through by (x + 6) ----- x + 16 = 1.5x + 9
7 = 0.5x
14 = x

check the answer choices with y = 2, z = 4:
a: 14
b: 3
c: 16
d: 10
e: 24

a wins