Question

pls help me with this its the last 2 days to turn in work and i dont know how
Admission to the Pie Eating Contest is $1.50 for children and $4 for adults. On a certain day, 2200 people came to watch and $5050 is collected. How many children and adults attended the Contest?
Show ALL work.

Let x = number of children

Let y = number of adults

A. Write 2 equations to model this system:

B. Solve the first equation for x (get the x alone on 1 side): 5 points

C. Use Substitution to solve the equations and determine how many adults and how many children attended

Answer 1

Number of people (P = 2200) is equal to number of children (x) plus number of adults (y) so:
P = x + y = 2200

Amount collected (A = $5050) is equal to the number of children times $1.50 plus the number of adults times $4. What does that equation look like?

Answer 2

uhh....idk do i multiply ?

Answer 3

can u help with part b and c pls thank u

Answer 4

Try writing out an equation with x, y, $1.50, $4.00, and $5050. You can do it.

Answer 5

uh x(1.50) * y(4.00)=5050 i really dont know how to :( i cant do it

Answer 6

x(1.50) * y(4.00)=5050 is \(almost \) the same as:
\(1.5x \color{red}{+} 4y=5050\)
It is a plus because we add up the amounts received to get $5050.

Answer 7

Can you find the second equation?

Answer 8

oh, @Valpey already gave it to you as the first equation:
x+y=2200 (meaning #children + #adults =2200 people)

Answer 9

B. Solve the first equation for x (get the x alone on 1 side):
This means that you need to isolate x from the first equation
x+y = 2200

Answer 10

x + y=2200
-1.5 -1.5=x ? .......

Answer 11

You may want to concentrate on part B, which says:
B. Solve the \(first\) equation for x (get the x alone on 1 side):
This means that you need to \(isolate\) x from the first equation
x+y = 2200
x=?

Answer 12

x=1.5

Answer 13

right?

Answer 14

x+y=2200
subtract y from either side, what do you get?

Answer 15

so substract 4from each side

Answer 16

yes, subtract \(\color{red}{y}\) from each side of the equality sign!

Answer 17

um so x+y=2200
-4 -4 like that ?

Answer 18

y does not equal 4! Both x and y represent the number of people (children and adults)
question says:
"
Let x = number of children
Let y = number of adults
"
so we don't know y yet. y is an unknown representing the number of adults that we are trying to find.
You have to subtract y as an entity, example
x+y = 2200
so whatever y stands for, the following equations are still valid
x+y-y=2200-y
x=2200-y
THis process is called isolating y because we have y only on the left-hand side.

Answer 19

thank u

Answer 20

thank u

Answer 21

so in part c
i would b making an equation out of the numbers and the variable right ?

Answer 22

\(Example\) of substitution:
given
x+y=10 .......(1)
2x+3y=25.....(2)

First isolate x:
x=10-y.....(1A)
Substitute means replace x (in the second equation) by the value of x in terms of y which we got from the first equation (1A)
2(10-y) + 3y = 25 .......(2A)
Now solve (2A) to get the value of y:
1. distribute
2*10 - 2y + 3y = 25
group like terms, and isolate y
3y-2y +20-20 = 25-20
y =5
Now, backsubstitute value of y into the first equation (1) to solve for x:
x+5 = 10
x = 10 - 5
x=5

You would proceed the same way to work on part C.