Question 192775
I am not sure what you doing here, but this is the way I would do it.
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1. To determine the number of deer in a game preserve, a conservation catches
 545 deer tags them and let them loose. Later, 836 deer are caught, 209 of them
 are tagged. How many deer are in the preserve? 
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The ratio of caught deer 209:836, same as 545 is to deer (d) running around 
{{{209/836}}} = {{{545/d}}}
cross multiply
209d = 545 * 836
209d = 455620
d = {{{455620/209}}}
d = 2180 deer in the preserve
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 2. Lisa can shovel snow from her driveway in 40 minutes.
 Jim can do the same job in 50 minutes. 
How long would it take Lisa and Jim to shovel the driveway if they work together.
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Let t = time required when they work together
Let the completed job = 1
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Each will do a fraction of the job that will add up to 1:
{{{t/40}}} + {{{t/50}}} = 1 
Multiply equation by 200 to get rid of the denominators, results:
5t + 4t = 200
9t = 200
t = {{{200/9}}}
t = 22.22 minutes working together
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Check using a calc:
{{{22.2/40}}} + {{{22.22/50}}} = 1 
.5555 + .4444 = .9999 ~ 1