1. The problem is to understand why the answer $r = 1.05$ makes sense in the equation $350r = 367.50$. 2. Recall that $r$ represents a multiplier applied to 350 to get 367.50. 3. Since $367.50$ is $350$ plus an additional $17.50$, we can write: $$367.50 = 350 + 17.50$$ 4. The additional $17.50$ is $5\%$ of $350$ because: $$0.05 \times 350 = 17.50$$ 5. Therefore, the multiplier $r$ is: $$r = 1 + 0.05 = 1.05$$ 6. This means multiplying $350$ by $1.05$ increases it by $5\%$, resulting in $367.50$. 7. Hence, the answer $r = 1.05$ makes sense because it represents a $5\%$ increase over $350$ to reach $367.50$. Final answer: $$r = 1.05$$