Select the correct answerThe sum of 3 numbers is 198.If the first number is 1/3rd of the second number and the third number is 5/7th of the first number, then what is the difference between the first number and second number?
Question
Select the correct answerThe sum of 3 numbers is 198.If the first number is 1/3rd of the second number and the third number is 5/7th of the first number, then what is the difference between the first number and second number?
Solution
Let's denote the three numbers as A, B, and C.
According to the problem, we have the following relationships:
- A + B + C = 198
- A = B/3
- C = 5A/7
We can substitute the second and third equations into the first one to solve for the variables:
Substituting A = B/3 into the first equation, we get: B/3 + B + 5B/21 = 198 Multiplying all terms by 21 to clear the fractions, we get: 7B + 21B + 5B = 4158 33B = 4158 B = 126
Substituting B = 126 into A = B/3, we get: A = 126/3 = 42
The difference between the first number (A) and the second number (B) is: B - A = 126 - 42 = 84
So, the difference between the first number and the second number is 84.
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