Question

You are the administrator of an annual essay contest scholarship fund. This year a $90,000 college scholarship is being divided between the top two contestants so that the winner receives five times as much as the runner-up. How much will each contestant receive (in dollars)?

runner-up amount :

winner amount:

Answer 1

Answer:

Runner-up: $15,000

Winner: $75,000

Step-by-step explanation:

Let's create an equation for this problem.

Let x=the amount the runner-up receives

Let 5x=the amount the winner receives

Then,

x+5x=90,000

6x=90,000

x=15,000

5x=75,000

Answer 2

Amount of scholarship received by the winner and runner-up using the equation is equal to $\ 75,000$ and $\ 15,000$ respectively.

What is the equation?

" Equation is defined as the representation of the relation between the variables and the number using the sign of equality."

According to the question,

Given,

Total amount of scholarship $=\ 90,000$

$'x'$ represents the amount of scholarship received by the runner-up

$'y'$ represents the amount of scholarship received by the winner

As per the given condition equation we have,

$x + y = \ 90,000$                            ________$(1)$

$y = 5x$                                           ________$(2)$

Substitute the value of $'y'$ in equation $(1)$ we get,

$x+ 5x = 90,000\\\\\implies 6x = 90,000\\\\\implies x = \ 15,000$

Therefore,

$y = 5 \times 15,000\\\\\implies y = \ 75,000$

Hence, the amount of scholarship received by the winner and runner-up using the equation is equal to $\ 75,000$ and $\ 15,000$ respectively.

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