Kate is allowed to work no more than 20 hours a week. she has already worked 13 hours this week. at most, how many more hours can she work? write an inequality and solve.

We'll call "k" the number of hours that Kate is allowed to work per week.

She can work no more than 20 hours a week, so k ≤ 20. So she can work 20, or less, but no more than 20.

But, she has already worked 13 hours.

So, k ≤ 20-13
k ≤ 7. So, Kate can work up to 7 more hours this week.