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ratio cross cancel method

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ratio cross cancel method

by shahab03 » Sun May 20, 2012 8:33 am
can someone please explain in detail how to do this problem using cross cancel method... i was able to do it by bringing all the values to same level but that takes too long would like to do it faster. thanks


At a certain school, the ratio of the number of second
graders to the number of fourth graders is 8 to 5, and
the ratio of the number of first graders to the number of
second graders is 3 to 4. If the ratio of the number of
third graders to the number of fourth graders is 3 to 2 ,
what is the ratio of the number of first graders to the
number of third graders?

(A) 16 to 15
(B) 9 to 5
(C) 5 to 16
(D) 5 to 4
(E) 4 to 5
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by Anurag@Gurome » Sun May 20, 2012 8:44 am
shahab03 wrote:can someone please explain in detail how to do this problem using cross cancel method... i was able to do it by bringing all the values to same level but that takes too long would like to do it faster. thanks


At a certain school, the ratio of the number of second
graders to the number of fourth graders is 8 to 5, and
the ratio of the number of first graders to the number of
second graders is 3 to 4. If the ratio of the number of
third graders to the number of fourth graders is 3 to 2 ,
what is the ratio of the number of first graders to the
number of third graders?

(A) 16 to 15
(B) 9 to 5
(C) 5 to 16
(D) 5 to 4
(E) 4 to 5
Let the number of 1st, 2nd, 3rd and 4th graders be A, B, C and D respectively.
Then we have to find A : C.

B/D = 8/5
A/B = 3/4
C/D = 3/2

Now B/D = 8/5 = (8 * 2)/(5 * 2) = 16/10
C/D = 3/2 = (3 * 5)/(2 * 5) = 15/10
A/B = 3/4 = (3 * 4)/(4 * 4) = 12/16

A/C = (A/B) * (B/D) * (D/C) = (12/16) * (16/10) * (10/15) = 12/15 = [spoiler]4/5[/spoiler]

The correct answer is E.
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by eagleeye » Sun May 20, 2012 8:49 am
Hi Shahab03:

I don't know what the cross cancel method is but this is how I did it and it didn't take more than 30 seconds. Let First, Second,Third, Fourth be A,B,C,D: then
we are given :
1. B/D = 8/5
2. A/B = 3/4
3. C/D = 3/2
we want A/C:
A/C = A/B * B/C = A/B * (B/D * D/C) = 3/4 * (8/5*2/3) = 4/5

Hence E

Let me know if this helps :)
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