Five friends compete in a dart-throwing contest. Each one has two darts to throw at the same circular target, and each individual's score is the sum of the scores in the target regions that are hit. The scores for the target regions are the whole numbers 1 through 10. Each throw hits the target in a region with a different value. The scores are: Alice—16 points, Ben—4 points, Cindy—7 points, Dave—11 points, and Ellen 17—points. Who hit the region worth 6 points?

Alice

Step-by-step explanation

Ben=1+3

Cindy=2+5

Dave=4+7

Alice=10+6

Ellen is 9+8

The answer is gonna be Alice because you can only use each number once.

POSSIBLE SCORES

Alice 16

6,10

7,9

(8+8 won't work because that would be a repeating number)

Ben 4

1,3

(2+2 won't work because that would be a repeating number)

Cindy 7

1,6

2,5

3,4

Dave 11

1,10

2,9

3,8

4,7

5,6

Ellen 17

7,10

8,9

Since the only possibilities for Ben is hitting 1 and 3, all other people can't hit 1 or 3.

Alice 16

6,10

7,9

Cindy 7

2,5

Dave 11

2,9

4,7

5,6

Ellen 17

7,10

8,9

Since the only possibilities for Cindy is hitting 2 and 5, all other people can't hit 2 or 5.

Alice 16

6,10

7,9

Dave 11

4,7

Ellen 17

7,10

8,9

Since the only possibilities for Dave is hitting 4 and 7, all other people can't hit 4 or 7.

Alice 16

6,10

Ellen 17

8,9

Ellen must have hit 8 and 9. Alice must have hit 6 and 10.

Alice hit 6 points.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.