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In a small sweet shop people usually buy...

In a small sweet shop people usually buy either one cake or one box of chocolate. One day the shop sold 57 cakes and 36 boxes of chocolates. How many customers were there that day if 12 people bought both a cake and a box of chocolates?

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To solve the problem step by step, we can follow these steps: ### Step 1: Identify the given values - Number of cakes sold (N(C)) = 57 - Number of boxes of chocolates sold (N(CH)) = 36 - Number of people who bought both cakes and chocolates (N(C ∩ CH)) = 12 ### Step 2: Use the formula for the union of two sets We need to find the total number of customers (N(C ∪ CH)), which can be calculated using the formula: \[ N(C ∪ CH) = N(C) + N(CH) - N(C ∩ CH) \] ### Step 3: Substitute the values into the formula Now, we substitute the values we have into the formula: \[ N(C ∪ CH) = 57 + 36 - 12 \] ### Step 4: Perform the calculations First, add the number of cakes and chocolates: \[ 57 + 36 = 93 \] Then, subtract the number of people who bought both: \[ 93 - 12 = 81 \] ### Step 5: Conclusion Thus, the total number of customers that day is: \[ N(C ∪ CH) = 81 \] ### Final Answer The total number of customers that day is **81**. ---
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