The product of two positive numbers is 189 and their quotient is \(\frac{3}{7}\). Find the sum of these numbers.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 30
Let the numbers be \(x\) and \(y\). Multiplying the product by the quotient makes \(y\) cancel and leaves \(x^{2}\).
\(xy=189\) (1)
\(\displaystyle\frac{x}{y}=\frac{3}{7}\) (2)
Multiplying (1) and (2), \(y\) cancels: \(\displaystyle x^{2}=189\times\frac{3}{7}=81\), so \(x=9\) (the numbers are positive)
From (1): \(y=189\div9=21\)
Sum \(=9+21=30\)