you work at a grocery store. your hourly wage is greater after 6pm than it is during the day. one week you work 20 daytime hours and 12 evening hours and earn $280. another week you work 30 daytime hours and 12 evening hours and earn a total of %276. what is your daytime rate? what is your evening rate?
Let x = daytime rate and y = evening rate.
20x + 12y = 280
Therefore x = (280 - 12y)/20
30x + 12y = 276
Use the same procedure as indicated in your previous post.
To solve this problem, we need to set up a system of equations based on the given information. Let's denote the daytime rate as D and the evening rate as E.
Based on the first week:
20D + 12E = $280 (Equation 1)
Based on the second week:
30D + 12E = $276 (Equation 2)
Now, we can solve this system of equations. There are multiple methods you can use, but for simplicity, let's use the method of substitution.
From Equation 1, we can isolate D:
20D = $280 - 12E
D = ($280 - 12E)/20
Substitute this expression for D into Equation 2:
30(($280 - 12E)/20) + 12E = $276
Now, we can solve for E:
840 - 36E + 240E = 5520
204E = 4680
E = 4680/204
E ≈ $22.94 (Evening rate)
Substitute this value of E back into Equation 1 to find D:
20D + 12($22.94) = $280
20D = $280 - $275.28
20D = $4.72
D ≈ $0.24 (Daytime rate)
Therefore, the daytime rate is approximately $0.24 and the evening rate is approximately $22.94.