Question

the product of two no.s is 1575 and their quotient is 9/7.find the numbers

Answer 1

let the number be x and y.
product of number xy= 1575
quotient x/y=9/7
$xy = 1575 \\ \frac{x}{y} = \frac{9}{7} \\ x = \frac{9y}{7} \\ put \: this \: value \: in \: above \: equation \\ ( \frac{9y}{7} )y = 1575 \\ 9 {y}^{2} = 1575 \times 7 \\ {y}^{2} = \frac{1575 \times 7}{9} \\ {y}^{2} = 175 \times 7 \\ {y}^{2} = 1225 \\ y = \sqrt{1225} \\ y = + 35 \\ y = - 35 \\ put \: the \: value \: of \: y \: in \: eq \\ xy = 1575 \\ x = \frac{1575}{35} = 45 \\ x = \frac{1575}{ - 35} = - 45$