Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
1) y + 3z
2) (y+z)/4
3) 2y + 3z
4) 3y + z
5) 3y + 4.5z
thanks
-B
ratios
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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
the original thread contains sundry followup comments, so you may want to go have a look at them.
--
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
Ron has been teaching various standardized tests for 20 years.
--
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Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron