one week you work 20 daytimes hours and 20 nightime hours, and earn $380. another week you work 30 daytime and 12 evening and earn $276

Question

What is daytime andwhat is nigtime rate?

Answer 1

Kahlee,

 

Y ou have a problem in two unknowns so you must have 2 independent equations to solve for them, which you do in this problem.

 

Let d = daytime rate in $ per hour

Let n = nighttime rate in $ per hour

 

Then  20d + 20n = 380 dividing thru by 2 to get 10d in first term:     10d + 10n = 190

and   30d + 12n = 276 dividing thru by -3 to get -10d in first term:  -10d  -   4n  = -92   

Adding the two equations eliminates the d unknown:   (10d - 10d) + (10n -4n)    = (190 - 92) = 98

 

So  6n = 98  and n = 98 / 6 = $ 16.33 per hour nighttime pay rate

and 10d = 190 - 10n = 190 -163.33 = 26.67,  so d = $ 2.67 per hour daytime rate

 

Also, instead of adding the modified equations, you could instead have used the method of substitution: solve the first one for d interns of n, and then substitute that for d in the second equation and solve for n, then back to solve for d.

 

That solves the math problem, but you wouldn't see such disparities in the real world, where the night pay rate may be 50% more or double the day rate, not six times! And the day rate is well below the minimum wage at around $7.50

So the problem writer should have picked coefficients that would produce results closer to the real world. 

Answer 2

Let d = daytime rate

Let n = nighttime rate

 

Compose the system of equations

 

20d + 20n = 380

30d + 12n = 276

 

Multiply the first equation by 3 and the second equation by 2. You get: 

 

60d + 60n = 1140

60d + 24n =  552

 

Subtract the two equations. You get:

 

36n = 588

 

n = $16.33/hr

d = $2.66/hr