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

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x, y - the numbers

The ratio of x to y is 2:3.
[tex]\frac{x}{y}=\frac{2}{3} \\ 3x=2y \\ x=\frac{2}{3}y[/tex]

Their product is 600.
[tex]xy=600 \\ \\ \hbox{subsitute } \frac{2}{3}y \hbox{ for x and solve for y:} \\ \frac{2}{3}y \times y=600 \\ \frac{2}{3}y^2=600 \\ y^2=600 \times \frac{3}{2} \\ y^2=900 \\ y=\pm \sqrt{900} \\ y=-30 \ \lor \ y=30 \\ \\ \hbox{the numbers are positive so y=30} \\ xy=600 \\ x \times 30=600 \\ x=\frac{600}{30} \\ x=20[/tex]

The numbers are 20 and 30.
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.
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