Question

Nicole makes $9.50 per hour working at an electronics company. She plans to buy a hand-held computer, the least expensive of which costs $245.60 and the most expensive of which costs $368.40. Write and solve an inequality describing how long Nicole will have to work to be able to buy a hand-held computer.

Please give me steps on how to solve this problem. THANK YOU.

Answer 1

26 ≤ x ≤ 39 where x is # of hours

Explanation:

If we call the number of hours she works x, Nicole will have made 9.50x after x hours. Therefore, we can write the following compound inequality:

245.60 ≤ 9.50x ≤ 368.40 (Note that we use ≤ instead of <; "at least/most" is denoted by ≤ or ≥)

Dividing the entire inequality by 9.50 (to get rid of the coefficient on x, we get about 26 ≤ x ≤ 39. We round up to the nearest integer because you can't really have, say, 25.69 hours in this context, you would have 26.