Subjects algebra

Coin Total D24163

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1. **State the problem:** Amir has 80 coins consisting of £1 and 50p coins in a ratio of 3:2. We need to find the total amount of money in pounds. 2. **Set up variables:** Let the number of £1 coins be $3x$ and the number of 50p coins be $2x$ because the ratio is 3:2. 3. **Write the equation for total coins:** $$3x + 2x = 80$$ 4. **Simplify the equation:** $$5x = 80$$ 5. **Solve for $x$:** $$x = \frac{80}{5} = 16$$ 6. **Find the number of each coin:** - £1 coins: $3x = 3 \times 16 = 48$ - 50p coins: $2x = 2 \times 16 = 32$ 7. **Calculate total money:** - Total from £1 coins: $48 \times 1 = 48$ pounds - Total from 50p coins: $32 \times 0.5 = 16$ pounds 8. **Add totals:** $$48 + 16 = 64$$ **Final answer:** Amir has 64 pounds in total.