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14 Aug 2019, 00:30
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84% (02:19) correct
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At a certain school, the ratio of the number of five-year-old's to the number of nine-year-old's is 12 to 5, and the ratio of the number of four-year-old's to the number of five-year old's is 3 to 4. If the ratio of the number of eight-year-old's to the number of nine-year-old's is 3 to 2, what is the ratio of the number of four-year-old's to the number of eight-year-old's?
A. 24 to 23
B. 11 to 6
C. 3 to 2
D. 6 to 5
E. 5 to 6
A. 24 to 23
B. 11 to 6
C. 3 to 2
D. 6 to 5
E. 5 to 6
Archit3110
14 Aug 2019, 03:10
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Bunuel
given
y5/y9= 2/5
y4/y5=3/4
y8/y9=3/2
we can re write ;
y9=2y8/3
y5/y8 = 12/5 * 2/3
y5= 8y8/5
so
y4/y8 = 3*8/4*5 ; 6/5
IMO D
16 Aug 2019, 18:29
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the ratio of the number of five-year-old's to the number of nine-year-old's is 12 to 5
5y to 9y
12k:5k
and the ratio of the number of four-year-old's to the number of five-year old's is 3 to 4
4y to 5y
3k:4k
Combine the above ratios, making 5y 12k in both (so multiply 4y by 3)
4y to 5y to 9y
9k:12k:5k
the ratio of the number of eight-year-old's to the number of nine-year-old's is 3 to 2
8y to 9y
3k:2k
We now want to combine that with the above ratio. The lowest common multiple of 2 and 5 (for 9y) is 10. So we need to double the numbers in the first ratio
4y to 5y to 9y
18k: 24k: 10k
and x5 the numbers in the second ratio
8y to 9y
15k:10k
To get combined
4y to 5y to 8y to 9y
18k: 24k: 15k:10k
what is the ratio of the number of four-year-old's to the number of eight-year-old's?
18k:15k
18:15
6:5
D
5y to 9y
12k:5k
and the ratio of the number of four-year-old's to the number of five-year old's is 3 to 4
4y to 5y
3k:4k
Combine the above ratios, making 5y 12k in both (so multiply 4y by 3)
4y to 5y to 9y
9k:12k:5k
the ratio of the number of eight-year-old's to the number of nine-year-old's is 3 to 2
8y to 9y
3k:2k
We now want to combine that with the above ratio. The lowest common multiple of 2 and 5 (for 9y) is 10. So we need to double the numbers in the first ratio
4y to 5y to 9y
18k: 24k: 10k
and x5 the numbers in the second ratio
8y to 9y
15k:10k
To get combined
4y to 5y to 8y to 9y
18k: 24k: 15k:10k
what is the ratio of the number of four-year-old's to the number of eight-year-old's?
18k:15k
18:15
6:5
D
