Gloria worked 27 hours in one week. The next week, the number of hours she worked decreased such that the ratio of hours worked during the first week to the number of hours worked during the second week is 3:2. How many hours did she work during the second week?

a) 12 hours
b) 18 hours
c) 15 hours
d) 9 hours

Using the provided ratio of hours worked, 3:2, and knowing she worked 27 hours the first week, we find that Gloria worked 18 hours the following week by setting up a proportion and solving for the unknown number of hours. Therefore, Gloria worked 18 hours during the second week, which corresponds to option b).

Explanation:

If Gloria worked 27 hours in one week and the following week she worked fewer hours in such a way that the ratio of the first week to the second week is 3:2, we need to determine how many hours she worked in the second week. To do this, we set up a proportion using the ratio 3:2 where 3 represents the 27 hours she worked in the first week.

Let the number of hours Gloria worked in the second week be x hours.
Set up the ratio as 3:2 = 27:x.
To find x, cross-multiply and solve for x: 3x = 2 × 27.
Calculate: 3x = 54.
Divide by 3 on both sides: x = 54 / 3.
x = 18 hours.