Subjects algebra

Milk Price

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1. **Stating the problem:** Lisa’s Quick Stop sells milk at a price 2% below the main grocery store. We are given Lisa’s prices for 8 weeks and want to find the corresponding main grocery store prices. 2. **Understanding the relationship:** If Lisa’s price is 2% less than the main store price, then Lisa’s price is 98% (100% - 2%) of the main store price. 3. **Expressing mathematically:** Let $P_m$ be the main store price and $P_l$ be Lisa’s price. Then: $$P_l = 0.98 \times P_m$$ 4. **Finding main store price:** Rearranging for $P_m$: $$P_m = \frac{P_l}{0.98}$$ 5. **Calculating main store prices for each week:** - Week 1: $\frac{2.30}{0.98} = 2.3469$ (approx) - Week 2: $\frac{2.42}{0.98} = 2.4694$ - Week 3: $\frac{2.36}{0.98} = 2.4082$ - Week 4: $\frac{2.49}{0.98} = 2.5408$ - Week 5: $\frac{2.24}{0.98} = 2.2857$ - Week 6: $\frac{2.36}{0.98} = 2.4082$ - Week 7: $\frac{2.42}{0.98} = 2.4694$ - Week 8: $\frac{2.49}{0.98} = 2.5408$ 6. **Final answer:** The main grocery store prices for the 8 weeks are approximately: $$[2.35, 2.47, 2.41, 2.54, 2.29, 2.41, 2.47, 2.54]$$ These prices are rounded to two decimal places for clarity.