Two positive numbers x and y are in the ratio a : b where 0 < a < b. If x + y = c then find the smaller of x and y in terms of a, b and c. Please leave explanation too please! :)
+23254 If x and y are in the ratio a:b, then x:y = a:b or x/y = a/b.
Since x + y = c, then y = c - x..
Since x/y = a/b and y = c - x, then, by substituting: x/(c - x) = a/b.
Cross multiplying: x(b) = a(c - x) ---> bx = ac - ax ---> ax + bx = ac ---> x(a + b) = ac
Dividing both sides by (a + b) ---> x = ac / (a + b)
+23254 If x and y are in the ratio a:b, then x:y = a:b or x/y = a/b.
Since x + y = c, then y = c - x..
Since x/y = a/b and y = c - x, then, by substituting: x/(c - x) = a/b.
Cross multiplying: x(b) = a(c - x) ---> bx = ac - ax ---> ax + bx = ac ---> x(a + b) = ac
Dividing both sides by (a + b) ---> x = ac / (a + b)
