The problem is called Skeeball Showdown and here it is. Steeball is a popular arcade game in which balls are rolled up a ramp and launched towards a target. Depending where it falls, each ball can score 10, 20, 30, 40 or 50 points. A player gets the same number of balls per game, no matter how well or poorly they score.

Kira and Dajuan decided to have a Skeeball contest. They each played one game to see who would get the highest score. A description of their contest follows:

- Kira scored as many 30's as Dauan did 20's.
- Dajuan scored one more 40 than he did 20.
- Kira scored the same number of 50' as she did 30's.
- Dajuan scored twice as many 30's as he did 20's.
- Kira scored one less than twice as many 20's as Dajuan did.
- Dajuan scored two more 40's than Kira did 10's.
- Kira scored the same number of 40's as she did 10's.

When it was all over, Dajuan had won by 10 points. Write and solve an equation to answer these two questions:

1) How many balls are rolled in a game of Skeeball?
2) What was the final score of the contest?

Help! Sincerely, (a new teacher with a question and no answer!)


Hi Jenny,

I let a be the number of times that Kira scored 30 points and then I drew up a table, read through the clues and filled in the values.

  Kira Dajuan
10 points a - 1  
20 points 2a - 1 a
30 points a 2a
40 points a - 1 a + 1
50 points a  
Total 6a - 3 4a + 1

We must have that they threw the same number of balls so 6a - 3 = 4a + 1. Solving for a gives a = 2.

Now find their scores.