Questions: Santiago swims several times per week in a lake near his home. Last summer, the lake's average water temperature was 20°C. This summer, the average water temperature was 7.7% warmer. What was the average temperature of the lake this summer? Round your answer to the nearest tenth. °C

Solution Steps

To find the average temperature of the lake this summer, we need to calculate the increase in temperature based on the given percentage and then add this increase to last summer's average temperature.

1. Calculate the increase in temperature by multiplying last summer's average temperature by the percentage increase (7.7%).
2. Add the calculated increase to last summer's average temperature to get this summer's average temperature.
3. Round the result to the nearest tenth.

To find the increase in temperature, we use the formula: \[ \text{Increase} = \text{Last Summer's Temperature} \times \left(\frac{\text{Percentage Increase}}{100}\right) \] Substituting the values: \[ \text{Increase} = 20.0 \times \left(\frac{7.7}{100}\right) = 1.54 \]

Next, we add the increase to last summer's average temperature: \[ \text{This Summer's Temperature} = \text{Last Summer's Temperature} + \text{Increase} \] Substituting the values: \[ \text{This Summer's Temperature} = 20.0 + 1.54 = 21.54 \]

Finally, we round the result to the nearest tenth: \[ \text{This Summer's Temperature (rounded)} = 21.5 \]

Final Answer