Math Question?

Question

Al and Bob decided to have a Skeeball contest. The ball can score 10,20,30,40,or50 pts.
1. Al scored as many 30's as Bob did 20's.
2. Bob scored one more 40 than he did 20's.
3. Al scored the same number of 50's as he did 30's.
4. Bob scored twice as many 30's as he did 20's.
5. Al scored one less than twice as many 20's as Bob did.
6. Bob scored two more 40's than Al did 10's.
7. Al scored the same number of 40's as he did 10's.

1. What was the final score (each)?.....
2. How many balls were rolled?

Please Explain....

Al lost by 10 pts.

Answer 1

A30 = B20
B40 = B20 + 1
A50 = A30 = B20
B30 = 2 * B20
A20 = 2 * B20 - 1
A10 = B40 - 2 = B20 - 1
A40 = A10 = B20 - 1

This is everything expressed in relationship to B20. Let's call that x:
A10 = x - 1
A20 = 2x - 1
A30 = x
A40 = x - 1
A50 = x

B10 = ?
B20 = x
B30 = 2x
B40 = x + 1
B50 = ?

B10 and B50 aren't specified, so are we to assume that they are 0?
B10 = 0
B50 = 0

We know that the number of balls for each should be equal:
A10 + A20 + A30 + A40 + A50 = B10 + B20 + B30 + B40 + B50

Al:
6x - 3
Bob:
4x + 1

Equate these:
6x - 3 = 4x + 1
2x = 4
x = 2

That means we have:
A10 = 1
A20 = 3
A30 = 2
A40 = 1
A50 = 2

Al's score = 1 * 10 + 3 * 20 + 2 * 30 + 1 * 40 + 2 * 50
= 10 + 60 + 60 + 40 + 100 = 270

B10 = 0
B20 = 2
B30 = 4
B40 = 3
B50 = 0

Bob's score 0 * 10 + 2 * 20 + 4 * 30 + 3 * 40 + 0 * 50
= 0 + 40 + 120 + 120 + 0 = 280

In summary,

Al scored 270
Bob scored 280

They each threw 9 balls.

Edit: I see you added a clue about Al losing by 10 points which is consistent with my answer. That seems to confirm my assumption that because A10 and A50 were unstated, that they are zero.