the admission fee at a small fair is $1.50 for children and $4.00 for adults.?

Question

on a certain day 2200 people enter the fair and $5050 is collected. How many children and how many adults have attendted

Answer 1

let x = no. of children
2200 - x = no. of adult
1.50 x + ( 2200 - x ) 4.00 = 5050
1.50 x + 8800 - 4 x = 5050
2.5 x = 3750
x = 1500 . . . . . . . . . . . . children
2200 - x = 700 . . . . . . adults

Answer 2

Substitution Method

Let

x = Children

y = Adults

2200 = Total number of children and adults

1.50 = Children admission fee

4.00 = adult admission fee

5050 = total fees collected

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x + y = 2200- - - - - - - - - - - -Equation 1
1.50x + 4.00y = 5050- - - - -Equation 2
- - - - - - - - - - - - -

isolate the y variable in equation 1

x + y = 2200

Transpose x

x + y - x = - x + 2200

y = - x + 2200

Substitute the y value into equation 2

- - - - - - - - -

1.50x + 4.00y = 5050

1.50x + 4.00(- x + 2200) = 5050

1.50x + ( - 4.00x + 8800) = 5050

1.50x - 4.00x + 8800 = 5050

Collect like terms

- 2.5x + 8800 = 5050

Transpose 8800

- 2.5x + 8800 - 8800 = 5050 - 8800

- 2.5x = 5050 - 8800

- 2.5x = - 3750

Divide both sides of the equation by - 2.5

- 2.5x / - 2.5 = - 3750 / - 2.5

x = - 3750 / - 2.5

x = 1500

Insert the x value into equation 1
- - - - - - - - - - -

x + y = 2200

1500 + y = 2200

Transpose 1500

1500 + y - 1500 = 2200 - 1500

y = 2200 - 1500

y = 700

INsert the y value into equation 1
- - - - - - - - -

Check for equation 1

x + y = 2200

1500 + 700 = 2200

2200 = 2200

- - - - - - - - - -

Check for equation 2

1.50x + 4.00y = 5050

1.50(1500) + 4.00(700) = 5050

2250 + 2800 = 5050

5050 = 5050

- - - - - - - - - --

Both equations balance

There are 1500 children and 700 adults

- - - - - - -s-

Answer 3

It's a lot easier to do it like this:

Assume all 2200 admissions were children: $3300.
But that leaves you $1750 short. The difference between an adult and a child is $2.50, which divides 700 times into 1750, so you must have 700 adults. Subtract to get 1500 children.

It also works if you assume all 2200 were adults: $8800. But that gives you $3750 too much. Divide that by $2.50, and you find you need 1500 children. Subtract to get 700 adults.

Answer 4

700 Adults and 1500 Children.

(700 * $4.00) + (1500 * $1.50) = $5050

And 700 + 1500 = 2200 People.

Hence Solved....

Answer 5

1000 adults
700 children

1000*4 + 700*1.5 = 4000+1050= 5050

Answer 6

Let x = adult at $4 and (2200-x) = children at $1.50
1.5(2200-x) + 4(x) = 5050
3300 - 1.5x + 4x = 5050
2.5x = 1750
x = 700
700 adults ($2800)
1500 children ($2250)
2800+2250 = 5050 check

Answer 7

1000 kids, 1200 adults