SOLUTION: horse is 2/3 as old as carabao, the difference between their ages is 4. how old is the carabao?

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Let H represent the age of the horse and C represent the age of the carabao. The problem tells
you that the horse's age is two-thirds of the age of the carabao. Therefore, the horse is
younger than the carabao. It also tells you that the difference in their ages is 4 years.
Therefore if we subtract the age of the horse from the age of the older carabao, the difference
is to be 4 years. In equation form this is:
.
C - H = 4
.
Then you are told that the age of the horse (H) is 2/3 the age of the older carabao.
In equation form this is:
.
H = (2/3)C
.
Notice now that you can use the fact that H = (2/3)C to substitute (2/3)C for H in the
equation that shows the difference in their ages to be 4. When you make that substitution
in the age difference equation, that equation becomes:
.
C - (2/3)C = 4
.
But C - (2/3)C is equal to (1/3)C. Therefore, the left side of this equation can be replaced
by (1/3)C to make the equation become:
.
(1/3)C = 4
.
You can now solve for C by either dividing both sides of this equation by (1/3) or by
multiplying both sides by 3. If you multiply both sides by 3 the left side becomes
just C and the right side becomes 4*3 = 12. So this equation is reduced to:
.
C = 12
.
Now you know that the age of the carabao is 12 years. And since the horse's age is two-thirds
of that you can multiply 2/3 times 12 to get H. (2/3) * 12 is equal to 24/3 and when you
divide 24 by 3 the answer is 8.
.
At this point you have the answer. The carabao is 12 and the horse is 8.
.
You can check by verifying that the difference in their ages (12 - 8) is 4 years and that
8 is 2/3 times 12.
.
Hope this helps you to understand the problem and provides you with an understandable
method of solving it.