Question

Find two positive numbers whose ratio is 2:3 and whose product is 600

Answer 1

First ratio - 2 second ratio - 3 sum of ratio - 2+3 = 5 first +ve no. = 2/5 × 600 240 ans. second +ve no. = 3/5 × 600 360 ans.

Answer 2

x, y - the numbers

The ratio of x to y is 2:3.

`(x)/(y)=(2)/(3) \\ 3x=2y \\ x=(2)/(3)y`

Their product is 600.

`xy=600 \\ \\ \hbox{subsitute } (2)/(3)y \hbox{ for x and solve for y:} \\ (2)/(3)y * y=600 \\ (2)/(3)y^2=600 \\ y^2=600 * (3)/(2) \\ y^2=900 \\ y=\pm √(900) \\ y=-30 \ \lor \ y=30 \\ \\ \hbox{the numbers are positive so y=30} \\ xy=600 \\ x * 30=600 \\ x=(600)/(30) \\ x=20`

The numbers are 20 and 30.