The equation x² - bx + 24 = 0 has two real solutions whose difference is 5. What is the value of b, given that both solutions are positive?

Let the roots be $r$ and $r + 5$. Their product is 24 (the constant term), so $r(r + 5) = 24$, which becomes $r^2 + 5r - 24 = 0$ and factors as $(r + 8)(r - 3) = 0$. Both roots must be positive, so $r = 3$ and the roots are 3 and 8. In $x^2 - bx + 24 = 0$, $b$ equals the sum of the roots: $b = 3 + 8 = 11$. A common wrong answer is $-11$, from using the other sign, which would give negative roots. Another is $5$, the difference of the roots, and a third is 24, the product.