Question

of two number is, 4 times the smaller one is less than 3 times the larger one by 5 . if the sum of the numbers is larger than 5 times their difference by 22, find the two numbers.?with soluction full

Answer 1

Let the smaller number be x

Let the larger number be y

Form the equations:

4 times the smaller one is less than 3 times the larger one by 5

⇒ 3y - 4x  = 5

The sum of the numbers is larger than 5 times their difference by 22

⇒ (y + x) - 5(y - x) = 22

⇒ y + x - 5y + 5x = 22

⇒ 6x - 4y = 22

⇒ 3x - 2y = 11

Putting the 2 equations together:

3y - 4x  = 5 -------------------  [ 1 ]

3x - 2y = 11 -------------------  [ 2 ]

[ 1 ] x 2 : 6y - 8x  = 10

[ 2 ] x 3 : 9x - 6y = 33

Find x:

[ 1 ] + [ 2 ] : x = 43

FInd y:

3y - 4x  = 5

3y - 4(43) = 5

3y - 172 = 5

3y = 177

y = 177 ÷ 3 = 59

Answer: The bigger number is 59 and the smaller number is 43