EIGHTH GRADE MATH PLEASE HELP!! 1. Tickets to the fair cost $7 for children and $14 for adults. On Wednesday, 178 people enter the fair and collected $1848. What number of children and what number of adults attended?

2. Tickets to the fair cost $5 for children and $11 for adults. On Tuesday, 164 people enter the fair and collected $1270. What number of children and what number of adults attended?

Ok first set some variables.

Lets call adults x

Lets call children y

Given: 2200 people attend the fair

using x and y write and equation to express this

x + y = 2200

Now lets look at what else we are told

Given: Child admission fee is $1.50

Adult admission fee is $4.00

The total amount collected is $5050.00

Now again using x and y write and equation to express this known information

4x + 1.5y = 5050

In other words $4 times the number of adults (x) plus $1.50 times the number of children (y) equals $5050

Ok so now we have a system of equations that we can use to solve for x and y

x + y = 2200

AND

4x + 1.5y = 5050

To solve the equations I will demonstrate the substitution method.

Take the first equation and set it equal to x

x + y = 2200

subtract y from both sides

x + y - y = 2200 - y

x = 2200 - y

Now since we have shown that x equals 2200-y we can substitute that for x in the second equation and solve for y

4x + 1.5y = 5050

4(2200-y) + 1.5y = 5050

multiply 4 across (2200-y)

8800 - 4y + 1.5y = 5050

combine like terms

8800 - 2.5y = 5050

subtract 8800 from both sides

8800 - 8800 - 2.5y = 5050 - 8800

-2.5y = -3750

divide both sides by -2.5

-2.5y/-2.5 = -3750/-2.5

y = 1500

1500 children attended the fair

Now use this answer to find x

Take the first equation and substitute y with 1500

x + y = 2200

x + 1500 = 2200

subtract 1500 from both sides

x + 1500 - 1500 = 2200 - 1500

x = 700

700 adults attended the fair

Check both answers in both equations

first equation:

x + y = 2200

700 + 1500 = 2200

2200 = 2200

Now the second equation:

4x + 1.5y = 5050

4(700) + 1.5(1500) = 5050

2800 + 2250 = 5050

5050 = 5050

Step-by-step explanation:

THIS MIGHT NOT BE RIGHT SO DONT TRUST IT

1, is So this means the answer is 81 children and 96 adults.

2,  250 $5 tickets and 100 $11 tickets were sold

Step-by-step explanation:

--- To solve this, you can use quadratics. x + y = 177 and 4x + 11y = 1380 are the equations to solve for x and y. 177 is the total amount of people who entered the fair, and 1380 is the total money earned. x is the amount of children entered, while y is the amount of adults entered. If we were to do 4(x + y = 177), the equation would become 4x + 4y = 708. Then, we minus the 2 equations together, eliminating the x so we can solve for y. So, the final equation is 7y = 672, meaning y = 96. If we bring this into the first equation, x + y = 177, we can find that x = 81.