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gmany

[tex]x:y=5:3\to\dfrac{x}{y}=\dfrac{5}{3}\qquad\text{cross multiply}\\\\3x=5y\qquad\text{divide both sides by 3}\\\\x=\dfrac{5}{3}y\\\\\text{substitute to the equation} \ x+y=56\\\\\dfrac{5}{3}y+y=56\\\\\dfrac{5}{3}y+\dfrac{3}{3}y=56\\\\\dfrac{5+3}{3}y=56\\\\\dfrac{8}{3}y=56\qquad\text{multiply both sides by 3}\\\\8y=3\cdot56\qquad\text{divide both sides by 8}\\\\y=3\cdot7\\\\y=21\\\\\text{substitute the value of y to the equation}\ x=\dfrac{5}{3}y\\\\x=\dfrac{5}{3}\cdot21=5\cdot7=35[/tex]


[tex]Answer:\ \boxed{x-y=35-21=14}[/tex]

altavistard

Let's rewrite the equation of ratios X:y=5:3 as:

x        5

---- = -----

 y       3

Cross-multiplying results in:  3x = 5y, or y = (3/5)x.

Substituting this last result into x + y = 56, we get:

x + (3/5)x = 56.

Remove the fraction by mult. all three terms by 5:  5x + 3x = 280.

Then 8x = 280, and x = 35.  If x = 35, then y = 56 - 35 = 21.

Summary:  x= 35, y = 21, and x - y = 35 - 21 = 14

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