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?

$44,970

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

she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

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