Quote:
On Sunday, in Alexa’s stable, the ratio of the number of ponies to the number of horses was 4:5. On Monday, she bought 35 more ponies and horses, then the ratio of ponies to horses became 5:8. Assuming that no animal left the stable or died and stable had ponies and horses only, what is the least number of horses that were there in the stable on Sunday?
A.35
B.55
C.60
D.65
E.70
Sunday.
Ponnie to horses ratio: \(4x/5x\), so horses must be multiple of 5. (All answers are multiple of 5, so no help here). Total number must be multiple of 9 (4+5)
Monday
Ponnie to horses ratio: \(5y/8y\). So total number must be multiple of 13
So equation looks as following \(9x+35 = 13y\)
My approach was to pick numbers.
Since the answers are arranged in ascending order, i prefer to start from C to choose direction.
C = 60 => On Sunday: \(5x = 60, =>9x = 60+(60/5)*4 =60+48 =108\)
On Monday: \(108+35 = 143\). Is 143 a multiple of 13? Yes = 13*11 =143. Looks like an answer, but we need to check A and B, to make sure that 60 is the least number
A: 35
Sunday \(5x=35, x=7, 9x=63\)
Monday \(63+35=98\) is 98 a multiple of 13? No, therefore cannot be A
B: 55
Sunday \(5x=55, x=11, 9x=99\)
Monday \(99+35=134\) is 134 a multiple of 13? No, therefore cannot be B
Therefore, ans is C
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