The coach of the Relay race team promised his athletes a reward if they win gold or silver. The reward is divided up relative to speed. Jenny got a sixth of the pot, Katherine a fifth. How big was the total reward sum, if Katherine got $ 1,499 more than Jenny?

Let’s assume J for Jenny, K for Katherine and R for reward. If Jenny gets a sixth of the pot, we can express it as J = 1/6 R. For Katherine’s fifth part we get K = 1/5 R. If Katherine receives $ 1,499 than Jenny, we know. K = J + 1,499. If you substitute K and J for their respective shares you come to this equation: 1/5 R = 1/6 R + 1,499. You can multiply it by thirty (5x6), so you get 6 R = 5R + 44,970 - > R = 44,970.