Question 68008: One hundred people attend the Wild West Snake Rodeo, and the admission receipts come to $100. Tickets are $5 per man, $2 per woman, and 10 cents per child. How many men, women, and children attended?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! One hundred people attend the Wild West Snake Rodeo, and the admission receipts come to $100. Tickets are $5 per man, $2 per woman, and 10 cents per child. How many men, women, and children attended?
:
Let the 3 types of people = x, y, z
:
x + y + z = 100
:
5x + 2y + .1z = 100
:
Two equations, three unknowns, some assumptions have to be made, since we are
dealing in integer dollars the number of children (z) has to be a multiple of 10
Also it is obvious that x < 20 and y < 50, I tried z = 60, no integer solution.
:
Try z = 70
:
x + y + 70 = 100
x + y = 100 - 70
x + y = 30
and
5x + 2y + .1(70) = 100
5x + 2y + 7 = 100
5x + 2y = 100 - 7
5x + 2y = 93
:
Mult x + y = 30 by 2 and subtract it from 5x + 2y = 93:
:
5x + 2y = 93
2x + 2y = 60
----------------subtracting eliminates y
3x = 33
x = 11 men at $5
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Find y using x + y = 30
11 + y = 30
y = 30 - 11
y = 19 women at $2
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And z = 70 at 10 cents
:
:
Check our solutions in both equations:
11 + 19 + 70 = 100
and
5(11) + (2)19 + .1(70) =
55 + 38 + 7 = 100
:
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