SOLUTION: Please help me solve this word problem: An electrician, a carpenter, and a plumber are hired to work on a house. The electrician earns $21 per hour, the carpenter $19.50 per hour

Question 146667This question is from textbook
: Please help me solve this word problem:
An electrician, a carpenter, and a plumber are hired to work on a house. The electrician earns $21 per hour, the carpenter $19.50 per hour, and the plumber $24 per hour. The first day on the job, they worked a total of 21.5 hr and earned a total of $469.50. If the plumber worked 2 more hours than the carpenter did, how many hours did each work? This question is from textbook

Found 2 solutions by scott8148, Alan3354:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
e+c+p=21.5

21e+19.5c+24p=469.5

p=c+2

substituting __ e+c+(c+2)=21.5 __ e=19.5-2c

substituting __ 21(19.5-2c)+19.5c+24(c+2)=469.5 __ (21*19.5)-42c+19.5c+24c+48=469.5 __ 1.5c=12 __ c=8

substituting __ p=(8)+2 __ p=10

substituting __ e+(8)+(10)=21.5 __ e=3.5
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
E = hours of electrician
C = carpenter
P = plumber
21E + 19.5C + 24P = 469.5
P = C + 2
E + P + C = 21.5
Substitute
E + (C+2) + C = 21.5
E + 2C = 19.5
Sub again
21E + 19.5C + 24(C+2) = 469.5
21E + 43.5C = 421.5
42E + 87C = 843
14E + 29C = 281
E = 19.5 - 2C
Sub again for E
14(19.5 - 2C) + 29C = 281
273 - 28C + 29C = 281
C = 8
P = 10
E = 3.5
Check - 8*$19.50 + 10*$24 + 3.5*$21 = $469.50

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