Select the correct answerOf 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.Options58564642

Let's denote the larger number as L and the smaller number as S.

From the problem, we have two equations:

1. 3L = 4S + 7
2. L + S = 6(L - S) + 4

We can simplify these equations to:

1. 3L - 4S = 7
2. L + S = 6L - 6S + 4

Rearranging the second equation gives:

2. -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 elimination method:

Multiply the first equation by 7 and the second equation by 4 to make the coefficients of S the same in both equations:

1. 21L - 28S = 49
2. -20L + 28S = 16

Now, add these two equations together:

21L - 20L = 49 + 16 L = 65

Substitute L = 65 into the first equation:

3*65 - 4S = 7 195 - 4S = 7 4S = 195 - 7 4S = 188 S = 188 / 4 S = 47

So, the larger number is 65 and the smaller number is 47.

But these numbers are not in the options. There might be a mistake in the problem or in the options.