You are the administrator of an annual essay contest scholarship fund. This year a $48,000 college scholarship is being divided between the top two contestants so that the winner receives three times as much as the runner-up. How much will each contestant receive?
To find out how much each contestant will receive, we need to divide the $48,000 scholarship between the winner and the runner-up.
Let's assume the amount the runner-up will receive is x dollars. According to the information given, the winner will receive three times as much as the runner-up, so the winner will receive 3x dollars.
Now, we know that the total scholarship amount is $48,000, which means the sum of the amounts received by the winner and the runner-up should add up to $48,000.
So, we can set up the following equation:
x + 3x = $48,000
Combining like terms, we have:
4x = $48,000
Now, let's solve the equation for x:
Dividing both sides of the equation by 4, we have:
x = $48,000 / 4
Simplifying the right side, we get:
x = $12,000
Therefore, the runner-up will receive $12,000.
Now, to find out how much the winner will receive, we can substitute the value of x back into the equation:
3x = 3 * $12,000 = $36,000
Therefore, the winner will receive $36,000.
In summary, the runner-up will receive $12,000, and the winner will receive $36,000.