A boy agreed to work one year for $240 and a horse. At the end of the seven months, he quit and received $100 and a horse. What was the value of the horse?
let x be the value of the horse in dollars
12 months wage is 240 + x => one month wage is (240 + x)/12
7 month wage is 100 + x => one month wage is (100 + x)/7
so we have:
(240 + x)/12 = (100 + x)/7
=> (240 + x)/12 - (100 + x)/7 = 0
=> (1680 + 7x - 1200 - 12x)/84 = 0
=> 1680 + 7x - 1200 - 12x = 0
=> 480 = 5x
=> x = 96
so the value of the horse is $96