You work at a grocery store. You hourly rate is greater after 6:00p.m. than it is during the day. One week you work 20 daytime hours and 20 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?

Question

You work at a grocery store. You hourly rate is greater after 6:00p.m. than it is during the day. One week you work 20 daytime hours and 20 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?

Answer 1

To find your daytime rate and evening rate, we can 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."

From the first week's information:
20D + 20E = $280

From the second week's information:
30D + 12E = $276

We now have a system of equations:

20D + 20E = $280 ...........(1)
30D + 12E = $276 ...........(2)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method:

Multiply equation (1) by 3 to make the coefficients of "D" in both equations the same:

60D + 60E = $840 ...........(3)

Subtract equation (2) from equation (3):

(60D + 60E) - (30D + 12E) = $840 - $276
30D + 48E = $564

Now we have the following equation:

30D + 48E = $564 ...........(4)

From equation (4), we can isolate "D":

30D = $564 - 48E
D = ($564 - 48E)/30

Now substitute the value of "D" in terms of "E" into equation (1):

20D + 20E = $280
20(($564 - 48E)/30) + 20E = $280

Simplify and solve for "E":

(20 * $564 - 20 * 48E)/30 + 20E = $280
( $11,280 - $960E)/30 + 20E = $280
$11,280 - $960E + 600E = $8,400

Combine like terms:

-360E = -$2,880

Divide both sides by -360:

E = $2,880 / $360
E = $8

Now substitute the value of "E" back into equation (1) to find "D":

20D + 20(8) = $280
20D + $160 = $280
20D = $280 - $160
20D = $120

Divide both sides by 20:

D = $120 / 20
D = $6

Therefore, your daytime rate is $6 per hour, and your evening rate is $8 per hour.

Answer 2

To find your daytime rate and evening rate, we can set up a system of equations.

Let's assume your daytime rate is D dollars per hour, and your evening rate is E dollars per hour.

According to the given information, you worked a total of 20 daytime hours and 20 evening hours and earned $280. This can be expressed as:
20D + 20E = 280 ---(Equation 1)

Similarly, in the second week, you worked 30 daytime hours and 12 evening hours and earned $276. This can be expressed as:
30D + 12E = 276 ---(Equation 2)

Now, we have two equations with two variables. We can solve this system of equations using different methods like substitution or elimination.

Let's solve it using the elimination method:

Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of 'D' the same:
(3) * (20D + 20E) = (3) * (280) ---(multiply Equation 1 by 3)
(2) * (30D + 12E) = (2) * (276) ---(multiply Equation 2 by 2)

This simplifies to:
60D + 60E = 840 ---(Equation 3)
60D + 24E = 552 ---(Equation 4)

Now, we can subtract Equation 4 from Equation 3 to eliminate the 'D' variable:
(60D + 60E) - (60D + 24E) = 840 - 552

This simplifies to:
36E = 288

Dividing both sides of the equation by 36:
E = 8

So, your evening rate is $8 per hour.

Now, substitute the value of E into Equation 1 or Equation 2 to find the daytime rate. Let's use Equation 1:
20D + 20(8) = 280

This simplifies to:
20D + 160 = 280

Subtracting 160 from both sides of the equation:
20D = 120

Dividing both sides of the equation by 20:
D = 6

So, your daytime rate is $6 per hour.

Therefore, your daytime rate is $6 per hour and your evening rate is $8 per hour.

Answer 3

set up an equation.. for example

d = daytime
e = evening

20d+20e=280

then 30d+12e=276

then you can use substitution and solve