Question 311293: at a fair the admission is $1.50 for children and $4.00 for adults. one day 2,200 people enter the fair and $5,050 is collected. how many children and how many adults attended.
Found 2 solutions by fractalier, palanisamy:
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Let x be the number of children.
Let y by the number of adults.
We have to set up two equations: One is for the number of people and the other is for the amount of money collected.
x + y = 2200
1.50x + 4.00y = 5050
We have to solve this system. I am going to do it by linear combination, that is, I am going to multiply the top equation by 4, so that, when I subtract the equations, the y's will drop out...here goes
4x + 4y = 8800
-(1.50x + 4.00y = 5050)
which yields
2.5x = 3750
and, then by dividing by 2.5, we get
x = 1500
Now substitute this back into the first equation, and
y = 700
Answer by palanisamy(496)  (Show Source):
You can put this solution on YOUR website! Let the number of children = x
And the number of adults = y
Total number x+y = 2,200 ...(1)
Total collection 1.5x+4y=5050 ...(2)
(1)*4=> 4x+4y = 8,800 ...(3)
(3)-(2)=> 2.5 x = 3,750
x = 3750/2.5
x = 1500
(1)=> 1500+y=2200
y=2200-1500
y=700
So, the number of children = 1500
And the number of adults = 700
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