Question

13. Mr. Smith teaches history and math classes. He has 25 students in both classes combined. He has 17 students in the math class and 15 students in the history class. Is it possible that 12 stu- dents are enrolled in both his history and his math classes?!

Answer 1

no

Explanation:

If m, h, b represent the numbers of students in Mr. Smith's math, history, and both classes, then we have ...

m + b = 17

h + b = 15

m + b + h = 25

Adding the first two equations and subtracting the third gives ...

(m+b) +(h+b) -(m+b+h) = (17) +(15) -(25)

b = 7 . . . . . . simplify

The number enrolled in both of Mr. Smith's classes is 7, not 12.

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Here, m and h represent the number of students enrolled in only one of Mr. Smith's classes, math or history, respectively.