1. **State the problem:** We have three scales balanced as follows: - Scale 1: 3 circles + 2 triangles = 9 squares - Scale 2: 3 circles + 3 triangles = 12 squares - Scale 3: 4 circles + 3 triangles = ? squares We need to find the number of squares (?) that balance the third scale. 2. **Set variables:** Let the weight of one circle be $c$, one triangle be $t$, and one square be $s$. 3. **Write equations from the first two scales:** $$3c + 2t = 9s$$ $$3c + 3t = 12s$$ 4. **Find $t$ in terms of $s$:** Subtract the first equation from the second: $$ (3c + 3t) - (3c + 2t) = 12s - 9s $$ $$ 3c - 3c + 3t - 2t = 3s $$ $$ t = 3s $$ 5. **Find $c$ in terms of $s$:** Substitute $t=3s$ into the first equation: $$ 3c + 2(3s) = 9s $$ $$ 3c + 6s = 9s $$ $$ 3c = 3s $$ $$ c = s $$ 6. **Calculate the weight on the left side of the third scale:** $$ 4c + 3t = 4s + 3(3s) = 4s + 9s = 13s $$ 7. **Find the number of squares needed to balance the third scale:** Since each square weighs $s$, the number of squares needed is 13. **Final answer:** 13 squares are needed to balance the third scale. (Note: The options given do not include 13, so the closest or intended answer might be 14 (option D), but mathematically it is 13.)