The variables $a$ and $b$ are inversely proportional. When the sum of $a$ and $b$ is 24, their difference is 6. What is $b$ when $a$ equals 5?
I know that inverse proportionality means $a \times b = k$ for some constant $k$. So I can use the given information to find $k$ and then use it to find $b$ when $a = 5$. When the sum of $a$ and $b$ is 24, I can write $a + b = 24$. When their difference is 6, I can write $a - b = 6$. I can add these two equations to eliminate $b$ and get $2a = 30$, or $a = 15$. Then I can plug $a = 15$ into either equation to get $b = 9$. So $k = a \times b = 15 \times 9 = 135$. Now I can use this value of $k$ and $a = 5$ to find $b$. I have $5 \times b = 135$, or $b = 27$. 