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A house-painting company charges a $376 base rate plus $12 per hour. Another painting company charges a base rate of $280 plus $15 per hour.

How long is a job for which both companies will charge the same amount?

a)   hours

 

b)  How much will the job in part "a" cost?

 Feb 2, 2015

Best Answer 

 #5
avatar+118609 
+6

Alright let's have a look

A house-painting company charges a $376 base rate plus $12 per hour. Another painting company charges a base rate of $280 plus $15 per hour.

 

Just say a job took 2 hours today.

the first company would charge    $376+  12*2 = 376+24  =  $400  

the second company would charge  280+   15*2 = 280+30 = $310      (this one is cheaper)

Do you understand so far?

 

We need to know how many hours would the painters work if the price ended up being the same

I don't know how many hours so I called that H

company one         376+12H     dollars

company two         280+15H      dollars

We need to know when these will be the same.

       376+12H   =280+15H 

subtract 12H from both sides

376 +12H-12H  = 280 +15H-12H

376   = 280 +3H

Take 280 of both sides

376-280=280+3H-280

96 = 3H

3H=96

H= 96/3 = 32 hours

 

now the first company will charge

376+12H = 376 +12*32 = 376 + 384 = $760

the second company will charge

280+15H = 280+15*32 = 280 + 480 = $760

GOOD they are the same - that proves that the answer is correct  

 Feb 2, 2015
 #1
avatar+118609 
+6

376+12H=280+15H

a)   solve for H

 

b)   Once you have H you cansub it back into  376+12H  or into   280+15H    to find the cost of this job.

The 2 answers should be the same :) 

 Feb 2, 2015
 #2
avatar
+5

i don't understand

 Feb 2, 2015
 #3
avatar+118609 
+5

you do not understand what I have already done? 

or you do not understand what do do next?

 Feb 2, 2015
 #4
avatar
+5

what 2 do next

 Feb 2, 2015
 #5
avatar+118609 
+6
Best Answer

Alright let's have a look

A house-painting company charges a $376 base rate plus $12 per hour. Another painting company charges a base rate of $280 plus $15 per hour.

 

Just say a job took 2 hours today.

the first company would charge    $376+  12*2 = 376+24  =  $400  

the second company would charge  280+   15*2 = 280+30 = $310      (this one is cheaper)

Do you understand so far?

 

We need to know how many hours would the painters work if the price ended up being the same

I don't know how many hours so I called that H

company one         376+12H     dollars

company two         280+15H      dollars

We need to know when these will be the same.

       376+12H   =280+15H 

subtract 12H from both sides

376 +12H-12H  = 280 +15H-12H

376   = 280 +3H

Take 280 of both sides

376-280=280+3H-280

96 = 3H

3H=96

H= 96/3 = 32 hours

 

now the first company will charge

376+12H = 376 +12*32 = 376 + 384 = $760

the second company will charge

280+15H = 280+15*32 = 280 + 480 = $760

GOOD they are the same - that proves that the answer is correct  

Melody Feb 2, 2015
 #6
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0

so how much will the job in part cost

 Feb 2, 2015

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