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In a group of 40 guests at a party. (1)/...

In a group of 40 guests at a party. `(1)/(5)` of the total number of guests opted for tomato soup, `(1)/(4)` of the guests chose to have vegetable soup, and the rest had fruit juice. Find the number of guests who had:
c. fruit juice

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To find the number of guests who had fruit juice, we can follow these steps: ### Step 1: Determine the total number of guests The total number of guests at the party is given as 40. ### Step 2: Calculate the number of guests who opted for tomato soup We know that \( \frac{1}{5} \) of the total guests opted for tomato soup. \[ \text{Number of guests for tomato soup} = \frac{1}{5} \times 40 = \frac{40}{5} = 8 \] ### Step 3: Calculate the number of guests who opted for vegetable soup Next, we know that \( \frac{1}{4} \) of the total guests chose vegetable soup. \[ \text{Number of guests for vegetable soup} = \frac{1}{4} \times 40 = \frac{40}{4} = 10 \] ### Step 4: Calculate the total number of guests who opted for soup Now, we can find the total number of guests who opted for either tomato or vegetable soup. \[ \text{Total guests for soup} = \text{Number of guests for tomato soup} + \text{Number of guests for vegetable soup} = 8 + 10 = 18 \] ### Step 5: Calculate the number of guests who had fruit juice To find the number of guests who had fruit juice, we subtract the total number of guests who opted for soup from the total number of guests. \[ \text{Number of guests for fruit juice} = \text{Total guests} - \text{Total guests for soup} = 40 - 18 = 22 \] ### Final Answer The number of guests who had fruit juice is **22**. ---
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