OlympiadBench / 2356 / The table below gives the final standings for seven of the teams in the English…

The table below gives the final standings for seven of the teams in the English Cricket League in 1998. At the end of the year, each team had played 17 matches and had obtained the total number of points shown in the last column. Each win W, each draw D, each bonus bowling point A, and each bonus batting point B received w,d,a and b points respectively, where w,d,a and b are positive integers. No points are given for a loss. Determine the values of w,d,a and b if total points awarded are given by the formula: Points =w×W+d×D+a×A+b×B.



Final Standings

|  | W | Losses | D | A | B | Points |
| :--- | :---: | :---: | :---: | :---: | :---: | :---: |
| Sussex | 6 | 7 | 4 | 30 | 63 | 201 |
| Warks | 6 | 8 | 3 | 35 | 60 | 200 |
| Som | 6 | 7 | 4 | 30 | 54 | 192 |
| Derbys | 6 | 7 | 4 | 28 | 55 | 191 |
| Kent | 5 | 5 | 7 | 18 | 59 | 178 |
| Worcs | 4 | 6 | 7 | 32 | 59 | 176 |
| Glam | 4 | 6 | 7 | 36 | 55 | 176 |

The table below gives the final standings for seven of the teams in the English Cricket League in 1998. At the end of the year, each team had played 17 matches and had obtained the total number of points shown in the last column. Each win $W$, each draw $D$, each bonus bowling point $A$, and each bonus batting point $B$ received $w, d, a$ and $b$ points respectively, where $w, d, a$ and $b$ are positive integers. No points are given for a loss. Determine the values of $w, d, a$ and $b$ if total points awarded are given by the formula: Points $=w \times W+d \times D+a \times A+b \times B$.



Final Standings

|  | $W$ | Losses | $D$ | $A$ | $B$ | Points |
| :--- | :---: | :---: | :---: | :---: | :---: | :---: |
| Sussex | 6 | 7 | 4 | 30 | 63 | 201 |
| Warks | 6 | 8 | 3 | 35 | 60 | 200 |
| Som | 6 | 7 | 4 | 30 | 54 | 192 |
| Derbys | 6 | 7 | 4 | 28 | 55 | 191 |
| Kent | 5 | 5 | 7 | 18 | 59 | 178 |
| Worcs | 4 | 6 | 7 | 32 | 59 | 176 |
| Glam | 4 | 6 | 7 | 36 | 55 | 176 |