Answer
$53\; lumens$.
Work Step by Step
Step 1:- Translate the statement to an equation.
Let the amount of light be $x$ lumens.
and the distance from the bulb is $d$.
From the question we have
$\Rightarrow x=\frac{k}{d^2}$ ...... (1)
Step 2:- Substitute all values into the equation to find the value of $k$.
The given values are $x=120\; lumens$ and $d=10\; feet$.
Substitute into the equation (1).
$\Rightarrow 120=\frac{k}{10^2}$
Simplify.
$\Rightarrow 120=\frac{k}{100}$
Multiply both sides by $100$.
$\Rightarrow 100\cdot 120=100\cdot\frac{k}{100}$
Simplify.
$\Rightarrow 12000=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=12000$ into the equation (1).
$\Rightarrow x=\frac{12000}{d^2}$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $B=6\;feet$ into equation (2).
$\Rightarrow x=\frac{12000}{15^2}$
Simplify.
$\Rightarrow x=53.33$
Hence, the amount of light is approximately $53\; lumens$.
