E01; Q-16; Horses and Ponies

[kannn]

A ranch has both horses and ponies. Exactly 5/6 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are Icelandic. If there are 3 more horses than ponies, what is the minimum number of horses and ponies combined on the ranch?

A. 12
B. 21
C. 27
D. 39
E. 57

[gmandar]

D:

1st equ: H =3+P
2nd equ: H+P = pick the number

[Jinx25]

Answer D, 39.

Solution:

x+x+3=

I used backsolving. Now the solution -3 has to be divisible by 2.
I tried 21 first.

2x= 18
x= 9

9 ponies * 5/6 doesnt work.

Next 39!

2x= 36
x= 18

18 ponies
5/6*18= 15 ponies had horseshoes.
2/3* 15= 10 ponies with horseshoes were Icelandic.

So we dont need to check 55. Answer is D!