ok I'm lost on this pls help!

Question

The coach of the rely race swim 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 Kathrine got $1,499 more than Jenny?

Answer 1

T = total = ?

 

J = amount Jenny got = T/6

 

K = amount Katherine got = T/5 ⇒ T = 5K

 

The above 2 equations imply J/K = (T/6)/(T/5) = 5/6 ⇒ J = (5/6)K

 

K = J + 1499

 

Solve the following 2 equations in 2 unknowns:

 

J = (5/6)K

K = J + 1499

 

Then

 

K = (5/6)K + 1499 ⇒ K = 8994

 

T = 5K = 5(8994) = 44970

 

Test the answer:

 

Is J = T/6?

 

J = (5/6)K = (5/6)(8994) = 7495

T/6 = 44970/6 = 7495 (good)

 

Is K = T/5?

 

T/5 = 44970/5 = 8994 = K (good)

 

The total pot was $44,970.

Answer 2

"The pot" and "the total reward" are important -- the other info is not.

 

Let:

    x = total pot

    J = amount Jenny got

    K = amount Katherine got

 

Translate:

  "Jenny got a sixth of the pot"     means    J = (1/6)x

  "Katherine a fifth"     means    K = (1/5)x

 

  "Kathrine got $1,499 more than Jenny"   means   K = $1,499 + J

 

Solve for x, "the total reward sum":

 

    K = $1499 + J

   (1/5)x = $1499   +    (1/6)x      [substitute values]

     6x  = $44970 + 5x        [multiply by LCM=30]

      x = $44,970       [subtract 5x from both sides]

 

Check:

   J = (1/6)x = $7495

   K = (1/5)x = $8994

   K = $1499 + $7495 = $8994  ? yes