Algebra Cowboy Problem

Question

A cowboy agreed to work for one year for 19,200 plus a horse. He quit after 7 months and was paid 10,450 but got to keep the horse. How many dollars was the horse worth if the salary pad reflects the fair proportion of his yearly salary?

(Hint: the answer is a four-digit whole number)

I keep getting a three digit number T__T. If someone could help that would be amazing and thank you in advance.

Answer 1

If you set up just the cash amount in a proportion, the horse will end up being worth 750. The trick in this question is that the horse is part of the payment in total, so it has to be used as a variable when setting up the proportion. It would look something like this:

19200 + h 10450 + h

--------------- = ---------------

12 7

Now you can solve for h, which will give you the value of the horse.

(19200 + h)(7) = (10450 + h)(12)

134400 + 7h = 125400 + 12h

9000 = 5h

h = 1800