Smallest Conversion 29F54A

1. **State the problem:** Robyn received €68.31 after converting pounds at one of two airports with different exchange rates. We need to find the smallest amount of pounds she could have converted. 2. **Identify the exchange rates:** - Airport 1: £1 = €1.15 - Airport 2: £1 = €1.08 3. **Set up the formulas:** Let $x_1$ be the amount in pounds converted at Airport 1, and $x_2$ be the amount in pounds converted at Airport 2. The euros received are given by: $$ \text{Euros} = \text{Pounds} \times \text{Exchange Rate} $$ So, $$ 68.31 = x_1 \times 1.15 \quad \text{or} \quad 68.31 = x_2 \times 1.08 $$ 4. **Calculate pounds for each airport:** For Airport 1: $$ x_1 = \frac{68.31}{1.15} $$ For Airport 2: $$ x_2 = \frac{68.31}{1.08} $$ 5. **Simplify each fraction:** $$ x_1 = \frac{68.31}{1.15} = \frac{68.31}{\cancel{1.15}} \times \frac{1}{\cancel{1}} = 59.4 $$ $$ x_2 = \frac{68.31}{1.08} = \frac{68.31}{\cancel{1.08}} \times \frac{1}{\cancel{1}} = 63.25 $$ 6. **Interpretation:** - At Airport 1, Robyn converted approximately £59.40. - At Airport 2, Robyn converted approximately £63.25. 7. **Answer:** The smallest amount of money she could have converted is **£59.40** at Airport 1.