Question

The sum of two numbers is 50. If the larger number is divided by the

smaller number we get 7/11. Find the numbers.

Answer 1

Set two equations:

• Number #1 = x
• Number #2 = y

`\left \{ {{x+y=50} \atop {(x)/(y)=(7)/(11) }} \right.`

Rearrange one of the equations to find the value of a variable:

`x+y=50\\x=50-y`

Substitute in that value into the other equation:

`(50-y)/(y)=(7)/(11)`

Cross-multiply & solve for y:

`7y=11(50-y) \\7y=550-11y\\7y+11y=550\\18y=550\\y=(550)/(18)=(275)/(9)`

Substitute in the value to the original equation to find x:

`(x)/((275)/(9))=(7)/(11) \\(9x)/(275)=(7)/(11) \\9(11)x=275(7)\\99x=1925\\x=(1925)/(99) =(175)/(9)`

Therefore, the answer will be:

• x =
  `(175)/(9)`

• y =
  `(275)/(9)`

You can check your answers by:

`(175)/(9) +(275)/(9) =(450)/(9) =50`

`((175)/(9) )/((275)/(9) ) =(175)/(9) *(9)/(275) =(175)/(275)=(7)/(11)`

Answer 2

x = 175/9

y = 275/9

Explanation:

Let the larger number be 'x' and smaller number be 'y'

sum of two numbers is 50.

x +y = 50 --------(I)

x = 50 - y -------------(II)

The larger number is divided by the smaller number we get 7/11.

`(x)/(y)=(7)/(11)\\\\`

Cross multiply,

11x = 7y

11x - 7y = 0 ------------(III)

Substitute x = 50 -y in equation (III)

11*(50-y) - 7y = 0

11*50 - 11*y - 7y = 0 {Distributive property}

550 - 11y - 7y = 0

550 - 18 y = 0 {Combine like terms}

Subtract 550 from both sides

- 18y = -550

Divide both sides by (-18)

y = -550/-18

y = 275/9

substitute y = 275/9 in equation (III)

`11x - 7*((275)/(9))=0\\\\11x-(1925)/(9)=0\\\\11x =(1925)/(9)\\\\x=(1925)/(9*11)\\\\x=(175)/(9)`