Question

Of two numbers, 4 times the smaller one is less than 3 times the larger one by 6. if the sum of the numbers is larger than 6 times their difference by 5, find the larger number.​

Answer 1

Answer:

Let x be the smaller number; and, y be the larger number.

Then, as per the question,.

3y - 4x = 5 (Eq.1)

Also,

x + y = 6 * (y - x) + 6

Or, x + y = 6y - 6x + 6

Or, 6y - y -6 x - x = - 6

Or, 5y - 7x = -6 (Eq. 2)

Multiplying bith sides of (( Eq. 1) by 5 ; and, both sides of (Eq. 2) by 3, we get:

15 y - 20 x = 25 (Eq 3)

15 y - 21 x = - 18 (Eq. 4)

Subtracting (Eq. 4) from (Eq. 3), we have :

x = 43

Substituting this value of x in ( Eq. 1), we have:

3 y - (4 * 43) = 5

Or, 3 y - 172 = 5

Or, 3 y = 5 + 172 = 177

Or, y = 177 / 3 = 59.

So, the smaller number is 43 and the larger number is 59.

Answer

Check:

(3 * 59) - (4 * 43) = 177 - 172 = 5 ✓

( Sum of the numbers) - 6 * ( Difference of the numbers)

= (43 + 59) - 6 * ( 59 - 43) = 102 - (6 * 16) = 102 - 96 = 6 ✓

Answer 2

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