1. **State the problem:** Vani wants to treat 12 friends with either bubble tea or ice-cream cones. Each bubble tea costs 3.20 and each ice-cream cone costs 2.40. She wants to spend no more than 30 in total. We need to check if she can do this if more friends want bubble tea than ice-cream cones. 2. **Define variables:** Let $b$ = number of friends who want bubble tea. Let $i$ = number of friends who want ice-cream cones. 3. **Write the constraints:** Since there are 12 friends total: $$b + i = 12$$ Since more friends want bubble tea than ice-cream cones: $$b > i$$ 4. **Write the cost inequality:** Total cost must be no more than 30: $$3.20b + 2.40i \leq 30$$ 5. **Express $i$ in terms of $b$:** From $b + i = 12$, we get: $$i = 12 - b$$ 6. **Substitute $i$ into the cost inequality:** $$3.20b + 2.40(12 - b) \leq 30$$ 7. **Simplify the inequality:** $$3.20b + 28.8 - 2.40b \leq 30$$ $$ (3.20b - 2.40b) + 28.8 \leq 30$$ $$0.80b + 28.8 \leq 30$$ 8. **Isolate $b$:** $$0.80b \leq 30 - 28.8$$ $$0.80b \leq 1.2$$ 9. **Divide both sides by 0.80:** $$b \leq \frac{1.2}{0.80}$$ $$b \leq 1.5$$ 10. **Interpret the result:** Since $b$ must be an integer number of friends, $b \leq 1$. But the condition is $b > i$ and $b + i = 12$, so $b$ must be more than 6 (since if $b > i$, and $b + i = 12$, then $b > 6$). 11. **Conclusion:** The maximum $b$ to keep cost under 30 is 1, but to have more bubble tea drinkers than ice-cream eaters, $b$ must be at least 7. Therefore, Vani cannot spend no more than 30 if more friends want bubble tea than ice-cream cones. **Final answer:** No, Vani will not be able to do so if more friends want bubble tea than ice-cream cones because the cost would exceed 30.