sarfarazkari39
Answered

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The sum of two numbers is 50. If the larger number is divided by the
smaller number we get 7/11. Find the numbers.

Sagot :

jessmzhou4

Answer:

Set two equations:

  • Number #1 = x
  • Number #2 = y

[tex]\left \{ {{x+y=50} \atop {\frac{x}{y}=\frac{7}{11} }} \right.[/tex]

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

[tex]x+y=50\\x=50-y[/tex]

Substitute in that value into the other equation:

[tex]\frac{50-y}{y}=\frac{7}{11}[/tex]

Cross-multiply & solve for y:

[tex]7y=11(50-y) \\7y=550-11y\\7y+11y=550\\18y=550\\y=\frac{550}{18}=\frac{275}{9}[/tex]

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

[tex]\frac{x}{\frac{275}{9}}=\frac{7}{11} \\\frac{9x}{275}=\frac{7}{11} \\9(11)x=275(7)\\99x=1925\\x=\frac{1925}{99} =\frac{175}{9}[/tex]

Therefore, the answer will be:

  • x = [tex]\frac{175}{9}[/tex]
  • y = [tex]\frac{275}{9}[/tex]

You can check your answers by:

[tex]\frac{175}{9} +\frac{275}{9} =\frac{450}{9} =50[/tex]

[tex]\frac{\frac{175}{9} }{\frac{275}{9} } =\frac{175}{9} *\frac{9}{275} =\frac{175}{275}=\frac{7}{11}[/tex]

devishri1977

Answer:

x = 175/9

y = 275/9

Step-by-step 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.

[tex]\frac{x}{y}=\frac{7}{11}\\\\[/tex]

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)

[tex]11x - 7*(\frac{275}{9})=0\\\\11x-\frac{1925}{9}=0\\\\11x =\frac{1925}{9}\\\\x=\frac{1925}{9*11}\\\\x=\frac{175}{9}[/tex]

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