Of two numbers ,3 times the larger one is greater than 4 times the smaller one by 7.Also, the sum of numbers is larger than 6 times their difference by 4.Find the largest number.Options46425856
Question
Of two numbers ,3 times the larger one is greater than 4 times the smaller one by 7.Also, the sum of numbers is larger than 6 times their difference by 4.Find the largest number.Options46425856
Solution
Let's denote the larger number as "L" and the smaller number as "S".
From the problem, we have two equations:
- 3L = 4S + 7
- L + S = 6(L - S) + 4
We can simplify these equations to:
- 3L - 4S = 7
- L + S = 6L - 6S + 4
Rearranging the second equation gives:
- -5L + 7S = 4
Now we have a system of two equations, and we can solve it using substitution or elimination method.
Let's use the substitution method. From the first equation, we can express L as L = (4S + 7) / 3.
Substitute L in the second equation:
-5((4S + 7) / 3) + 7S = 4 -20S/3 - 35/3 + 21S/3 = 4 S/3 - 35/3 = 4 S - 35 = 12 S = 47
Substitute S = 47 in the first equation:
3L = 4*47 + 7 3L = 188 + 7 3L = 195 L = 195 / 3 L = 65
So, the larger number is 65.
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