Answer to Question #325474 in Algebra for austyn

Question

The intensity of light​ (in foot-candles) varies inversely as the square of​ x, the distance in feet from the light source. The intensity of light 2 feet from the source is 80 ​foot-candles. How far away is the source if the intensity of light is 5 ​foot-candles?

Answer 1

Let $A$ be the numerator of our formula, and $I$ - intensity of light, then: $I=\frac{A}{X^2}$

If $X=2:80=\frac{A}4\implies A=320;$

If $I=5:5=\frac{320}{X^2}\implies X^2=\frac{320}5=64\implies X=8$ ​foot-candles.