SOLUTION: Thanks for the help in advance.. I need to know some steps :P Stuart agrees to a house-painting job for $900. He takes 4 days longer than expected,and he has earned $18.75 less

Question 214837: Thanks for the help in advance.. I need to know some steps :P
Stuart agrees to a house-painting job for $900. He takes 4 days longer than expected,and he has earned $18.75 less per day than expected. In how many days did he expect to complete the house? Answer is 12 days.
Found 2 solutions by checkley77, ankor@dixie-net.com:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
900/x-900/(x+4)=18.75
(900(x+4)-900x))/x(x+4)=18.75
(900x+3600-900x)/(x^2+4x)=18.75
3600=18.75(x^2+4x) divide everything by 18.75
192=x^2+4x
x^2+4x-192=0
x^2+4x-192=0
(X+16)(X-12)=0
X-12=0
X=12 DAYS PLANNED
12=4 ACTUAL DAYS SPENT PAINTING.
PR00F:
900/12-900/16=18.75
75-56.25=18.75
18.75=18.75

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Stuart agrees to a house-painting job for $900.
He takes 4 days longer than expected,and he has earned $18.75 less per day than expected.
In how many days did he expect to complete the house?
:
Let t = no. of days expected to paint the house
then
(t+4) = no. of actual days
:
Expected daily pay:
then
Actual daily pay:
;
Expected daily pay - Actual daily pay = 18.75
- = 18.75
Multiply equation by t(t+4), results:
900(t+4) - 900t = 18.75t(t+4)
:
900t + 3600 - 900t = 18.75(t^2 + 4t)
:
900t - 900t + 3600 = 18.75t^2 + 75t
:
Arrange as a quadratic equation
18.75t^2 + 75t - 3600 = 0
:
Simplify, divide by 18.75
t^2 + 4t - 192 = 0
:
(t + 16)(t - 12) = 0
Positive solution
t = 12 days is original no. of days

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