Question 1060291
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Kermit has agreed to paint Miss Piggy's house for $640.00. Unfortunately, it took Kermit 20 hours longer to paint the house 
than he had planned and he earned $1.60 per hour less than he had previously calculated. 
How much was Kermit's anticipated hourly wage to paint Miss Piggy's house?
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Let "a be Kermit's anticipated hourly wage, in dollars.
Then his real hourly wage was (a-1.6) dollars.

So, Kermit originally planned to complete the job in {{{640/a}}} hours.
But in reality he spent {{{640/(a-1.6)}}} hours.

The difference is 20 hours. It gives you an equation

{{{640/(a-1.6)}}} - {{{640/a}}} = 20.

To solve it, multiply both sides by a*(a-1.6). You will ge

640a - 640(a-1.6) = 20a(a-1.6).

{{{20a^2 -32a - 1024}}} = 0,

{{{5a^2 - 8a - 256}}} = 0,

{{{a{1,2]}}} = . . . {{{(8 +- 72)/10}}}.

The positive solution is a = 8.

<U>Answer</U>.  Kermit's anticipated hourly wage of $8.

<U>Check</U>.   {{{640/8}}} = 80 hours.  {{{640/(8-1.6)}}} = {{{640/6.4}}} = 100.  100 - 80 = 20.  Correct !
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Solved.