Factory Production Problem: Solving 1/3 Ratio with 700-Unit Constraint

To solve this problem, follow these steps:

• Step 1: Identify that $x = \frac{1}{3} y$ and substitute into the inequality $x + y < 700$.
• Step 2: Rewrite the inequality as $\frac{1}{3} y + y < 700$.
• Step 3: Combine and simplify terms: $\frac{4}{3} y < 700$.
• Step 4: Solve for $y$ by multiplying both sides by $\frac{3}{4}$: $y < 525$.
• Step 5: Substitute back to find $x$: Since $x = \frac{1}{3} y$, $x < \frac{1}{3} \times 525 = 175$.

Thus, we conclude that the production of factory A, $x$, is less than 175 cartons per day.