pullagurla wrote: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 � rst 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 � rst 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
To combine ratios, any element common to more than 1 ratio needs to be represented by the same value in each ratio.
In the problem above:
2nd:4th = 8:5
3rd:4th = 3:2
The 4th graders are common to each ratio, so we want them to be represented by the same value in each ratio. Since 5 and 2 are factors of 10, let's rewrite the ratios so that the 4th graders are represented by 10 in each ratio:
2nd:4th = 8:5 = 16:10
3rd:4th = 3:2 = 15:10
To continue:
1st:2nd = 3:4
2nd:4th = 16:10
The 2nd graders are common to each ratio, so we want them to be represented by the same value in each ratio. Since 4 and 16 are factors of 16, let's rewrite the first ratio so that the 4th graders are represented by 16:
1st:2nd = 3:4 = 12:16
Now all the ratios can be combined:
1st:2nd:3rd:4th = 12:16:15:10
So 1st:3rd = 12:15 = 4:5
The correct answer is E.
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