QUICK HELP ME! seven children in a family like apples, 6 children like bananas, and 5 children like peaches. four children like both apples and bananas, 3 children like both apples and peaches, 2 children like both peaches and bananas, and one child likes all three. how many children are in the family

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  10

Step-by-step explanation:

1 child likes all three

4 like apples and bananas, so 4-1 = 3 like apples and bananas only

3 like apples and peaches, so 3-1 = 2 like apples and peaches only

2 like peaches and bananas, so 2-1 = 1 like peaches and bananas only

7 like apples, but 3+2+1 like one or more other fruits, so 1 likes apples only

6 like bananas, but 3+1+1 like one or more other fruits, so 1 likes bananas only

5 like peaches, but 2+1+1 like one or more other fruits, so 1 likes peaches only

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1 + 1 + 1 = 3 like exactly 1 fruit;

3 + 2 + 1 = 6 like exactly 2 fruits;

1 likes exactly 3 fruits.

The total number of children is 3 + 6 + 1 = 10.

Assuming all the referenced children are in the family, there are 10 children in the family.

a. is correct