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The average weight of 5 crates is 250 pounds. The 2 lightest

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The average weight of 5 crates is 250 pounds. The 2 lightest [#permalink] New post 09 Feb 2007, 11:00
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1. The average weight of 5 crates is 250 pounds. The 2 lightest crates weigh between 200 and 205 pounds each, and the 2 heaviest weigh between 300 and 310 pounds each. If the weight of the fifth crate is x pounds, then x is expressed by which of the following?
A. 220 <= x <= 250
B. 230 <= x <= 260
C 240 <= x <= 270
D. 250 <= x <= 270
E. 260 <= x <= 280

2.Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?
A. 1.5
B. 1.7
C. 2.3
D. 2.5
E. 3.0
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 [#permalink] New post 09 Feb 2007, 11:30
1) question

The average weigth of 5 crates is 250. so the sum of the weigths is 1250
2 ligther crates weigth 200-205, so the sum of the weigths must be between 400-410
2 heviest weigth 300-310 so the sum is 600-620

Total weigth = 1250

The weight of the remaining crate must be between:

400+600=1000; 410+620=1030
1250-1000=250 and 1250-1030=220
x must be between 220 and 250

A
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 [#permalink] New post 09 Feb 2007, 11:51
2) question

I would suggest to construct a table on mixture problems:
You have to find X

A: 0.15x of alcohol 0.85x of other stuff TOTAL x
B: 0.5y of alcohol 0.5y of other stuff TOTAL y

A+B: 1.2 liters of alcohol 2.8 liters of other stuff TOTAL 4 liters

Now you simply construct the equation:

one equation: 0.15x+0.5y=1.2......multiply by -2
second eqation: x+y=4

-0.3x-y=-2.4
x+y=4

Add both together

0.7x=1.6
x=2.3 approximately....

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Re: PS [#permalink] New post 09 Feb 2007, 13:15
jet1445 wrote:
2.Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?
A. 1.5
B. 1.7
C. 2.3
D. 2.5
E. 3.0


Another approach for this question:
when combining liquids, I always use this rule: Vsum %sum = Va %a + Vb %b
Note: V=volumn

put numbers from question into function
4 x 30/100 = Va x 15/100 + Vb x 50/100
Since Va+Vb=4; so Vb=4-Va
4 x 30/100 = Va x 15/100 + (4-Va) x 50/100
Va=2.3
Anwser is C
Re: PS   [#permalink] 09 Feb 2007, 13:15
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The average weight of 5 crates is 250 pounds. The 2 lightest

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