You are the administrator of an annual essay contest scholarship fund. This year a $75,000 college scholarship is being divided between the top two contestants so that the winner receives four times as much as the runner-up. How much will each contestant receive (in dollars)?
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@ math helper i posted a question can you help it is pre algebra
Well, if the winner receives four times as much as the runner-up, we can assign the amount the runner-up receives as "x." That means the winner receives 4 vezes x. And since the total scholarship amount is $75,000, we can write an equation:
x + 4x = 75,000.
Combining like terms, we have 5x = 75,000.
Dividing both sides by 5, we find that x = 15,000.
So the runner-up will receive $15,000, and the winner will receive four times that amount, which is $60,000.
To find out how much each contestant will receive, let's break down the problem step by step.
Let's assume the amount the runner-up receives is 'x'. According to the problem, the winner will receive four times as much as the runner-up. So the amount the winner receives is 4 times 'x', which can be written as 4x.
Now, the sum of the amounts received by the winner and the runner-up should be equal to $75,000. We can write this as an equation:
x + 4x = 75000
Combining like terms:
5x = 75000
Next, we can solve for 'x' by dividing both sides of the equation by 5:
x = 75000 / 5
x = 15,000
Therefore, the runner-up will receive $15,000.
To find out how much the winner will receive, we can substitute the value of 'x' back into the original equation:
4x = 4 * 15,000 = $60,000
Therefore, the winner will receive $60,000.
So, the runner-up will receive $15,000 and the winner will receive $60,000.
runner-up to get x
winner to get 4x
x + 4x = 75000
5x = 75000
x = 15000
winner gets 4x or 60,000, runner-up gets x or 15,000