D The prize money for a competition is shared between the winner and the runner-up in the ratio 3: 1. The winner received

Question

D The prize money for a competition is
shared between the winner and the runner-up
in the ratio 3: 1.
The winner received £250 more than the
runner-up.
What was the total prize money?

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Thiên Ân 4 years 2021-08-11T21:44:17+00:00 2 Answers 40 views 0

Answers ( )

  1. yenoanh
    0
    2021-08-11T21:46:03+00:00
    Reply

    Answer:

    Total amount = £500

    Step-by-step explanation:

    Let the amount for the runner up be = x

    Let the amount for winner be =  x + 250

    Let the total amount be x + x + 250 = 2x + 250

    Ratio of  the amount is 3 : 1

    Sum of the ratio = 3 + 1  = 4

    Amount for the winner is

                                         \frac{3}{4} \ of \ (2x + 250) = (x + 250)\\\\\frac{3}{4}\times(2x + 250) = x + 250\\\\\frac{6x}{4} + \frac{750}{4} = x + 250\\\\\frac{6x}{4} - x = 250 - \frac{750}{4}\\\\\frac{6x - 4x}{4} = \frac{1000 - 750}{4}\\\\\frac{2x}{4} = \frac{250}{4} \\\\2x = 250\\\\x = 125

    Therefore, Amount won by runner – up = x = £125

                           Amount won by winner = x + 250 = 125  + 250 = £375

    Therefore, total amount = 375 + 125 = £500

  2. Neala
    0
    2021-08-11T21:46:16+00:00
    Reply

    Answer: 333.3

    Step-by-step explanation:

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