Question

X:y=5:3 and x+y=56
what is the value off x-y

Answer 1

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

Answer 2

`x:y=5:3\to(x)/(y)=(5)/(3)\qquad\text{cross multiply}\\\\3x=5y\qquad\text{divide both sides by 3}\\\\x=(5)/(3)y\\\\\text{substitute to the equation} \ x+y=56\\\\(5)/(3)y+y=56\\\\(5)/(3)y+(3)/(3)y=56\\\\(5+3)/(3)y=56\\\\(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=(5)/(3)y\\\\x=(5)/(3)\cdot21=5\cdot7=35`

`Answer:\ \boxed{x-y=35-21=14}`