Question

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?

Answer 1

Answer: $44,970

Step-by-step explanation:

1) Translate the statments to algebraic language

i) reward = unknwon = x

ii) Jenny got a sixth of the pot ⇒ (1/6)x

iii) Katherine a fifth ⇒ (1/5)x

iv) Katherine got $ 1,499 more than Jenny ⇒ (1/5)x = 1,499 + (1/6)x

2) Solve the equation:

i) start: (1/5)x = 1,499 + (1/6)x

ii) subtraction property: (1/5)x - (1/6)x = 1,499

iii) multiply by the least common denominator: 5×6 = 30

30x/5 - 30x/6 = 1,499×30

iv) do the operations: 6x - 5x = 44,970

v) combine like terms: x = 44,970

3) Verify the results:

(1/6)x = (1/6) ($44,970) = $ 7,495

(1/5)x = (1/5) ($44,970) = $ 8,994

$7,495 + $1,499 = $ 8,994

$ 8,994 = $ 8,994 ⇒ check

Answer 2

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.