Solving this Word Problem

Question

A man bought x boxes of doughnuts for 3.49 each. He paid with a $50 bill and received the correct amount of change. If he received more than $10 but less than $20, what inequality would represent the number of boxes of doughnuts he could have bought?

Answer 1

10 < 50 - 3.49x < 20

subtract 50

-40 < -3.49x < -30

multiply by -1, which reverses the direction of the inequality signs

40 > 3.49x > 30

divide by 3.49

40/3.49 > x > 30/3.49

11.46 > x > 8.6

round up, and down

12 > x > 8

x> 8

and

x < 12

the number of donut boxes purchased is either

9, 10 or 11

assuming no partial boxes