solving algebraic equations

Question

A part time moved regular pay rate is $60 an hour.if the work involves going up and down stairs, his rate increases to$90 an hour.In one week,he earned $1,380 and worked 20 hours. How many hours did he work at each rate?

Answer 1

Let x = the number of regular hours worked 

 

y = the number of hours traveling the stairs

 

x + y = 20 (total hours in the week)

 

60x + 90y = 1380

 

Solve the first equation for y

 

y = 20 - x

 

Plug this into the second equation

 

60x + 90(20 - x) = 1380

60x + 1800 - 90x = 1380

-30x + 1800 = 1380

-30x = -420

x = 14

 

So y = 20 - 14 = 6

 

He worked 14 regular hours and 6 hours traveling the stairs

Answer 2

60x+90(20-x)=1380

60x+1800-90x=1380

-30x+1800=1380

-30x=1380-1800

-30x=-420

30x=420

3x=42

x=42/3

x=14 hours at $60 and 6 hours at $90