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Brums [2.3K]
3 years ago
9

You are the administrator of an annual essay contest scholarship fund. This year a $80,000 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)? runner-up amount : winner amount:
Mathematics
1 answer:
Lana71 [14]3 years ago
3 0

Answer:

Runner Up Amount=$16,000

Winner Amount=$64,000

Step-by-step explanation:

Amount of the college's scholarship=$80,000

The fund is being divided between the top two contestants so that the winner receives four times as much as the runner-up.

Therefore: we can say it is being divided into 5 parts where the winner gets 4 parts and the runner up gets 1 part, i.e in the ratio 4:1.

Runner Up Amount=\dfrac{1}{5}X\$ $80,000=\$16000

Winner Amount=\dfrac{4}{5}X\$ $80,000=\$64000

The winner gets $64,000 and the runner up gets $16,000.

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Answer:

Max exercises 13 hours a week, and Sasha 7.

Step-by-step explanation:

To find the number of hours each of them exercises during the week, we solve the system of equations.

In the second equation:

x = 4y - 15

Replacing in the first equation:

x + y = 20

4y - 15 + y = 20

5y = 35

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y = 7

So Sasha exercises 7 hours per week.

Max:

x + y = 20

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x = 13

Max exercises 13 hours a week.

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