SOLUTION: When several boys tried to divide a sum of money by giving 10 dollar to each boy,7 boy got nothing.when each boy took 9 dollar,the had 7 dollar left over.what is the sum of the nu

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: When several boys tried to divide a sum of money by giving 10 dollar to each boy,7 boy got nothing.when each boy took 9 dollar,the had 7 dollar left over.what is the sum of the nu      Log On


   

Question 550116: When several boys tried to divide a sum of money by giving 10 dollar to each boy,7 boy got nothing.when each boy took 9 dollar,the had 7 dollar left over.what is the sum of the number of money and the number of boys?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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When several boys tried to divide a sum of money by giving 10 dollars to each boy, 7 boys got nothing.
When each boy took 9 dollars, they had 7 dollars left over.
What is the sum of the number of money and the number of boys?
:
Let a = total amt of money
Let b = no. of boys involved
:
Equation for each statement:
:
"When several boys tried to divide a sum of money by giving 10 dollars to each boy, 7 boys got nothing."
a%2F%28%28b-7%29%29 = 10
a = 10(b-7)
a = 10b - 70
:
"When each boy took 9 dollars, they had 7 dollars left over."
%28%28a-7%29%29%2Fb = 9
a - 7 = 8b
a = 9b + 7
:
In the 1st equation, replace a with (9b+7)
9b + 7 = 10b - 70
7 + 70 = 10b - 9b
b = 77 boys
:
Find a
a = 9b + 7
a = 9(77) + 7
a = 693 + 7
a = $700 is the amt
;
:
Check this in the 1st equation
a = 10b - 70
700 = 10(77) - 70
700 = 770 - 70; confirms our solution of: 77 boys, $700