Subjects algebra

Bread Margarine Prices 281821

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

Bread Margarine Prices 281821


1. **State the problem:** Akosua bought 5 loaves of bread and 3 sachets of margarine for a total of 8. A few days later, she bought 2 loaves of bread and 6 sachets of margarine for a total of 5.60. We need to find the price of one loaf of bread and one sachet of margarine. 2. **Set variables:** Let $b$ be the price of one loaf of bread. Let $m$ be the price of one sachet of margarine. 3. **Write the system of equations:** From the first purchase: $$5b + 3m = 8$$ From the second purchase: $$2b + 6m = 5.60$$ 4. **Solve the system:** Multiply the second equation by 5 to align bread coefficients: $$10b + 30m = 28$$ Multiply the first equation by 2: $$10b + 6m = 16$$ 5. **Subtract the second from the first:** $$(10b + 30m) - (10b + 6m) = 28 - 16$$ $$24m = 12$$ $$m = \frac{12}{24} = 0.5$$ 6. **Find $b$ by substituting $m=0.5$ into first equation:** $$5b + 3(0.5) = 8$$ $$5b + 1.5 = 8$$ $$5b = 8 - 1.5 = 6.5$$ $$b = \frac{6.5}{5} = 1.3$$ 7. **Answer:** Price of one loaf of bread is $1.3$ and one sachet of margarine is $0.5$. 8. **Check options:** None of the options exactly match $1.3$ or $0.5$, but the closest is $1.80$ which is not correct. Therefore, the exact prices are: - Bread: $1.3$ - Margarine: $0.5$