Liams cricket team scored 220 runs,
Liam scored 10 more runs than Brogan and 15 more than shannon
amy scored six runs less than brogan and eight more than emily
how many runs did shannon score
please i cried on this question i need help and im not going to just guess every number in the counting range and perform some medical operation on it there has to be another way to do this
Liam's runs --- x
Brogran's runs --- x-10
Shanno's runs --- x - 15
Amy ---- x-10 - 6 = x - 16
emily --- x-16 - 8 = x - 24
x+x-10+x-15 + x-16 + x-24 = 220
5x = 285
x = 57
so Lima has 57 runs
Brogan has 47 runs
Shannon has 42 runs
Amy has 41 runs
emily has 33 runs
All works out
thanks mathhelper
L = B + 10
L = S + 15
A = B - 6
A = E+ 8
L + S + B + A + E= 220
S + 15 + S + B +A + E = 220
B = L - 10
B = S + 15 - 10 = S + 5
S + 15 + S + S+5 + A + E = 220
3 S + 20 + A + E = 220
3 S + (B-6) + E = 200
3 S + (S+5-6) + (A-8) = 200
4 S - 1 + (B-6-8) = 200
4 S - 15 + B = 200
4 S - 15 + (S+5) = 200
5 S - 10 = 200
5 S = 210
S = 42
CHECK MY ARITHMETIC !
Never mind checking, we agree :)
To solve this problem, we can break it down step by step and derive the answer systematically.
1. Start by assigning variables to the unknown quantities mentioned in the problem statement. Let's use the following variables:
- Shannon's score: S
- Liam's score: L
- Brogan's score: B
- Amy's score: A
- Emily's score: E
2. From the given information, we can establish the following relationships:
- Liam scored 10 more runs than Brogan: L = B + 10
- Liam scored 15 more runs than Shannon: L = S + 15
- Amy scored six runs less than Brogan: A = B - 6
- Amy scored eight runs more than Emily: A = E + 8
3. We also know that the total score of the team is 220 runs:
- L + B + A + S + E = 220
Now, let's substitute the established relationships into the equation for the total score:
(B + 10) + B + (B - 6) + (B + 15) + (B - 6 + 8) = 220
Simplifying the equation, we get:
5B + 21 = 220
Subtracting 21 from both sides of the equation:
5B = 199
Finally, dividing both sides by 5:
B = 39.8
Since scores are typically measured in whole numbers, we can conclude that Brogan's score is 40.
Now, we can find the score of Shannon using the relationship L = S + 15:
40 + 10 = S + 15
50 = S + 15
Subtracting 15 from both sides:
S = 35
Therefore, Shannon scored 35 runs.