SOLUTION: 6500 us were divided equally among a certain number of persons. had there been 15 more persons, each would have got 30 us less. find the original number of persons.

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Question 550387: 6500 us were divided equally among a certain number of persons. had there been 15 more persons, each would have got 30 us less. find the original number of persons.
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
i dont know what a (us) is other than my country..lol but i will just say they are dollars($)
p= persons , x= amount per person
6500=px
6500=%28p%2B15%29%28x-30%29
the equations above come straight from the problem, the more word problems you do the easier it will become to recognize the equations
6500%2Fp=x
use substitution methed
6500=%28p%2B15%29%28x-30%29 foil
6500=%28px%2B15x-30p-450%29 substitute x
6500=%28p%286500%2Fp%29%2B15%286500%2Fp%29-30p-450%29
6500=6500%2B97500%2Fp-30p-450add like terms
450=97500%2Fp-30p multiply by p
450p=97500-30p%5E2 organize in ax^2+bx+c=0
30p%5E2%2B450p-97500=0 take the 30 out
30%28p%5E2%2B15p-3250%29 find 2 numbers that multiply to get -3250 and add to get +15
5*5*5*2*13=3250, 5*13=65 5*5*2=50, 65*-50=-3250 , 65-50=+15
30%28p%2B65%29%28p-50%29=0
p=-65p=50 p cant be negative so answer is highlight%2850%29
6500%2Fp=x
6500%2F50=x
130=x
check
6500=%28p%2B15%29%28x-30%29
6500=%2850%2B15%29%28130-30%29
6500=%2865%29%28100%29
6500=6500
correct