Maxing out

Algebra Level 3

$\large{ \begin{cases}x + 2y < 30 \\ 3x+ y < 26 \end{cases}}$

Let $x$ and $y$ be positive integers satisfying the system of inequality above.

Let the largest possible value of $x$ be $U$ and the largest possible value of $y$ be $V$ .

(Obviously, if $x = U$ , $y$ cannot simultaneously be equal to $V$ .)

Find $U + V$

1 solution

Denton Young
Jul 23, 2016

The largest value of $x$ occurs when $y = 1$ . Then $x = 8$ is the maximum, so $U = 8$

The largest value of $y$ occurs when $x = 1$ . Then $y = 14$ is the maximum, so $V = 14$

8 + 14 = 22