express compound inequality

Question

Iota charges $8.00 per hour and $5.00 material fee to build a fence. If she earns between $29.00 and $52.00,how many hours does she work? Express your answer as a compound inequality

Answer 1

 

$29 <= 8.00 * t + $5.00 <= $52  <--- where t is the number of hours worked

 

29 - 5 <= 8t <= 52 - 5  <--- subtracts 5 from both sides; decimal digits not necessary;

                                            neither is the dollar sign:  $1 can be factored out and cancelled

 

24 <= 8t <= 47

 

24/8 <= 8t/8 <= 47/8  <--- divides both sides by 8; 

 

3 <= t <= 47/8 = 5 and 7/8 hours = 5 hours 52 minutes 30 seconds