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

Factory A produces 1/3 of factory B's productivity, so A is smaller. Write $x = \frac{1}{3}y$, not the other way around. The fraction goes with the smaller quantity.

We substitute $x = \frac{1}{3}y$ into $x + y < 700$ to get one variable. This gives us $\frac{1}{3}y + y = \frac{4}{3}y < 700$, which we can solve directly.

Label clearly from the start! Read the problem: 'factory A produces 1/3 of factory B' means A is smaller. Write this relationship first, then proceed with the math.

Test with numbers: if A produces 170 cartons, then B produces $170 \times 3 = 510$ cartons. Total: 170 + 510 = 680 < 700 ✓. This confirms A < 175 is correct.

Because we have an inequality (<), not an equation (=). The problem gives us a constraint ('less than 700'), so our answer must also be a range, not a specific value.