Answer: So the total score was 8.
Step-by-step explanation:
Let's call the total score "x".
The highest score was 2/7 of the total score:
x * 2/7 = highest score
The next highest score was 2/7 of the remainder, which is x - highest score:
(x - highest score) * 2/7 = next highest score
The difference between the two scores is 8 runs:
highest score - next highest score = 8
We can substitute the expressions for highest score and next highest score in terms of x into the above equation:
x * 2/7 - (x - x * 2/7) * 2/7 = 8
Expanding and simplifying the equation:
x * 2/7 - x * 2/7 + x * 2/7 * 2/7 = 8
x * (2/7 + 2/7 * 2/7) = 8
x = 8 / (2/7 + 2/7 * 2/7)
Calculating the denominator:
2/7 + 2/7 * 2/7 = 2/7 + 4/49 = 46/49
Finally, substituting the denominator back into the expression for x:
x = 8 / 46/49
Cross multiplying to simplify the fraction:
49x = 8 * 49
Solving for x:
x = 8 * 49 / 49
x = 8
So the total score was 8.
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Answers & Comments
Answer: So the total score was 8.
Step-by-step explanation:
Let's call the total score "x".
The highest score was 2/7 of the total score:
x * 2/7 = highest score
The next highest score was 2/7 of the remainder, which is x - highest score:
(x - highest score) * 2/7 = next highest score
The difference between the two scores is 8 runs:
highest score - next highest score = 8
We can substitute the expressions for highest score and next highest score in terms of x into the above equation:
x * 2/7 - (x - x * 2/7) * 2/7 = 8
Expanding and simplifying the equation:
x * 2/7 - x * 2/7 + x * 2/7 * 2/7 = 8
x * (2/7 + 2/7 * 2/7) = 8
x * (2/7 + 2/7 * 2/7) = 8
x * (2/7 + 2/7 * 2/7) = 8
x = 8 / (2/7 + 2/7 * 2/7)
Calculating the denominator:
2/7 + 2/7 * 2/7 = 2/7 + 4/49 = 46/49
Finally, substituting the denominator back into the expression for x:
x = 8 / 46/49
Cross multiplying to simplify the fraction:
49x = 8 * 49
Solving for x:
x = 8 * 49 / 49
x = 8
So the total score was 8.