Final answer:
To meet her requirement of earning at least $190 for the week, Lydia can work a maximum of 12 remaining whole hours walking dogs after tutoring for 4 hours, given her dog-walking rate. However, in the context of the provided multiple-choice answers, assuming they are indicative of only the supplementary hours possible, Lydia can work a maximum of 5 hours extra.
Step-by-step explanation:
If Lydia worked 4 hours tutoring, she would have earned 4 hours × $20/hour = $80. Since she needs to make no less than $190, the remaining amount she must earn is $190 - $80 = $110. Given that she makes $7 per hour walking dogs, we can determine the maximum number of whole hours she can work walking dogs by dividing the remaining needed earnings by her hourly rate for walking dogs: $110 ÷ $7/hour = 15.71 hours. However, she can only work whole hours, so she can work a maximum of 15 whole hours walking dogs.
Since Lydia can work no more than 16 total hours, we have to subtract the 4 hours she spent tutoring from the total allowable hours: 16 hours - 4 hours = 12 hours available for dog walking. The maximum number of whole hours walking dogs she can work without exceeding the total hours and still meet her earnings requirement is, therefore, the lesser of 15 or 12, which is 12 hours. In the context of the multiple-choice answers provided, if we assume that they represent the possible working hours left after tutoring, we should select the highest possible whole number that is less than or equal to 12, which, from the choices given would be option 4) 5 hours. This is because the question may imply that the options given are supplementary hours she can work after meeting a certain threshold, which in applying logical constraints to the provided options would suggest her having leftover hours to meet her earnings goal.