Word Problem

Question

Mike works 58 hours a week.  He gets paid $7.00 an hour at job a and $8.00 hour at job b. He brings home $428 a week before taxes, then how man hours does he work at each job?

 

Answer 1

The total number of hours work for both jobs is 58, thus the equation is: 

 

a + b = 58, just assigning some variables to the two jobs. 

 

The number of hours worked at job A times the pay rate plus the hours worked at job B times the pay rate equals the total pay of $428. 

 

The equation looks like this: 

 

$7.00a + $8.00b = $428 

 

The constraint is the total number of hours worked for both jobs can not exceed 58. Thus, we plug the constrain into the second equation, 

 

$7.00a + $8.00(58 - a) = $428 

 

We solve and get: 

 

$7.00a + $464 - $8.00a = $428 

-$a = - $36

a = 36 hours, thus b = 22 hours 

 

Answer 2

let a=hours at job a; let b=hours at job b  a +b = 58 hours.  b = 58 - a

 

7(a) + 8(b) = 428  

 

7(a) + 8(58-a) =428

7a + 464 -8a =428

-a = -36

a=36  36* 7 = 252

58 - 36 = 22

22 * 8 = 176

 

176 +252 = 428