1. **State the problem:** We need to find the price of a wallet and a belt given sales data for two months. 2. **Define variables:** Let $w$ be the price of one wallet and $b$ be the price of one belt. 3. **Write the system of equations:** From last month: $$71w + 47b = 8309$$ From this month: $$93w + 76b = 11822$$ 4. **Use elimination to solve:** Multiply the first equation by 76 and the second by 47 to align coefficients of $b$: $$76(71w + 47b) = 76 \times 8309$$ $$47(93w + 76b) = 47 \times 11822$$ Which gives: $$5396w + 3572b = 631484$$ $$4371w + 3572b = 555434$$ 5. **Subtract the second equation from the first to eliminate $b$:** $$ (5396w + 3572b) - (4371w + 3572b) = 631484 - 555434 $$ $$ (\cancel{5396w} - \cancel{4371w}) + (\cancel{3572b} - \cancel{3572b}) = 76050 $$ $$ 1025w = 76050 $$ 6. **Solve for $w$:** $$ w = \frac{76050}{1025} $$ $$ w = 74 $$ 7. **Substitute $w=74$ into the first original equation:** $$ 71(74) + 47b = 8309 $$ $$ 5254 + 47b = 8309 $$ $$ 47b = 8309 - 5254 $$ $$ 47b = 3055 $$ 8. **Solve for $b$:** $$ b = \frac{3055}{47} $$ $$ b = 65 $$ **Final answer:** The boutique charges $74 for a wallet and $65 for a belt.