You are the administrator of an annual essay contest scholarship fund. This year a $88,200 college scholarship is being divided between the top two contestants so that the winner receives six times as much as the runner-up. How much will each contestant receive?
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To determine how much each contestant will receive, follow these steps:
Step 1: Let x represent the amount received by the runner-up.
Step 2: According to the given information, the winner will receive six times as much as the runner-up. Therefore, the amount received by the winner will be 6x.
Step 3: The total scholarship amount is $88,200. Thus, the sum of the amounts received by the runner-up and the winner should equal $88,200.
Step 4: Set up the equation: x + 6x = $88,200.
Step 5: Combine like terms: 7x = $88,200.
Step 6: Solve for x by dividing both sides of the equation by 7: x = $12,600.
Step 7: Substitute the value of x back into the equation to find the amount received by the winner: 6x = 6($12,600) = $75,600.
Step 8: The runner-up will receive $12,600, and the winner will receive $75,600.
To determine how much each contestant will receive, we need to divide the scholarship fund between the winner and the runner-up based on the given criteria.
Let's assume the amount received by the runner-up is x (in dollars). According to the given information, the winner will receive six times the amount of the runner-up. Therefore, the amount received by the winner is 6x (in dollars).
The total scholarship fund is $88,200, which means the sum of the amounts received by the runner-up and the winner should equal this total. We can represent this information in an equation:
x + 6x = $88,200
Combining like terms, we get:
7x = $88,200
To solve for x, we divide both sides of the equation by 7:
x = $88,200 / 7
x ≈ $12,600
Therefore, the runner-up will receive approximately $12,600.
As we determined earlier, the winner will receive six times the amount of the runner-up. Thus, the winner will receive:
6x = 6 * $12,600
≈ $75,600
Therefore, the winner will receive approximately $75,600.
To summarize:
- The runner-up will receive approximately $12,600.
- The winner will receive approximately $75,600.
divide the total into 7 equal shares.
The winner gets six of those shares, the runner-up gets one.