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Some people agree to share in the cost of buying a boat.  If ten of them later decide not to buy in, each of those remaining would have to chip in one dollar more.  If the sole payment actually occurs after an additional fifteen people drop out, each of those ultimately remaining has to pay two dollars more than he would have had to pay had only the first ten dropped out.  How many people originally agreed to buy a boat?

 Dec 7, 2019
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Original number of buyers = x

 

Price of boat = xy

after 10 drop out  price becomes  (x-10)(y+1)

after 15 more drop out  (x-25)(y+1+2)     all three of these amounts are equal (the price of the boat)

 

xy-10y+x-10  = xy +3x - 25y -75=xy

x-10y -10 = 3x-25y-75=0

 

System of equations becomes:  (solve for 'x' )

x-10y-10=0

3x-25y-75=0     multiply first equation  by -2.5

-2.5x+25y+25=0  add them together

.5x-50 =0

x=100 original buyers         100-10y-10=0    90 = 10y y = 9 price of boat per person  (TOTAL PRICE $900)

 Dec 7, 2019

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