Question 37: Find two numbers x and y, knowing that: \(\dfrac{x}{2} = \dfrac{y}{5}\) and xy = 10

Calling the common value of the ratios \(\dfrac{x}{2} \) and \(\dfrac{y}{5}\) is \(k\), we have:

\(\dfrac{x}{2}=\dfrac{y}{5}=k\)

Derive \(x = 2k; y = 5k\)

Since \(xy = 10\) \( 2k.5k = 10\)

\(\Rightarrow 10{k^2} = 10 \Rightarrow {k^2} = 1 \Rightarrow k = \pm 1\)

With \(k = 1\) then \( x = 2.1=2;y =5.1= 5\)

With \(k = -1\) then \(x = 2.(-1)= – 2;y =5.(-1)= – 5\)

Answer: \( x =2;y = 5\) or \(x = – 2;y = – 5\).