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3 votes
Ben has 50 toys. 15 of them are new and 9 are his favorites; 2 are new and favorites.

Ben is giving away all the toys that are neither new nor favorites. How many toys
does Ben give away?

1 Answer

3 votes

Answer:

28 toys

Explanation:

Ben has 50 toys, of which 15 are new, 9 are favorites, and 2 are new and favorites. You want to know the number that are neither new nor favorite.

Groupings

The number of new toys includes (new and favorite) and (new and not favorite). That is ...

15 = 2 + new and not favorite

So ...

new and not favorite = 15 -2 = 13

Likewise, the number of favorite toys includes (new and favorite) and (not new and favorite). That is ...

9 = 2 + not new and favorite

not new and favorite = 9 -2 = 7

Donated

The total of 50 toys includes ...

total = (new and favorite) + (new and not favorite) + (not new and favorite) + (not new and not favorite)

50 = 2 + 13 + 7 + (not new and not favorite)

Then the number of (not new and not favorite) is ...

not new and not favorite = 50 -2 -13 -7 = 28

These are the toys that Ben gives away.

Ben gives away 28 toys.

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