Math Questions Please.?

Question

Hi everyone, I have a few Algebra questions I have to do for a assignment..I did not study this properly because I broke my leg and was away for a while (bummer)..please of you can also explain it to me I would greatly appreciate it...

Students from the local high school are selling tickets to the town's annual carnival. Adult admission is $5.00 and child admission is $2.50. Two hours after the carnival opens its first day, 440 tickets have been sold, totaling $1900. How many adults and how many children entered the carnival during the first two hours it was open?...
A.)293 adults, 147 children...
B.)320 adults, 120 children...
C.)220 adults, 220 children...
D.)380 adults, 760 children...
Question2..
Use substitution to solve the system of equations given by y = 2x and 5x + y = 7...
A.)(1, 2)...
B.)(2, 4)...
C.)(2, 3)...
D.)(2, -3)..
Question 3...
Use elimination to solve the system of equations given by 3x - 2y = 10 and 5x + 2y = 6...
A.)(0, 0)..
B.)(-2, -2)..
C.)(2, 2)..
D.)(2, -2).

Answer 1

1. A + C =440
5A +2.5C=$1900

-5A - 5C =-2200
5A +2.5C = 1900
---------------------
-2.5C = -300
c=120 A = 440-120=320

2. y=2x
5x+y = 7

5x+2x = 7
7x = 7
x=1 y = 2

3. 3x-2y=10
5x + 2y = 6
-----------------
8x = 16
x = 2
5(2)+2y = 6
10+2y=6
2y = -4
y = -2

Answer 2

let

x = childs admission

y = adults admission

2.5x = cost for childs admission

5 = cost for adult admission

1900 = Total cost collected

- - - - - - - - - - - - - - - - - -

x + y = 440- - - - - - - -Equation 1
2.5x + 5x = 1900- - - - -Equation 2
- - - - - - - - - - - -

Substitute Method

x + y = 440

x + y - 4 = 440 - x

y = 440 - x

Insert the y value into equation 2

- - - - - - - - - - - - - - - - - - - - -

2.5x + 5y = 1900

2.5x + 5(440 - x) = 1900

2.5x + 2200 - 5x = 1900

- 2.5 + 2200 = 1900

- 2.5 + 2200 - 2200 = 1900 - 2200

- 2.5x = - 300

- 2.5x/- 2.5 = - 300?- 2.5

x =- 300 / - 2.5

x = 120

The answer is x = 120

Insert the x value into equation 1

- - - - - - - - - - - - -- - - -- - - - - -

x + y = 440

`120 + y = 440

120 + y - 120 = 440 - 120

y = 320

The answer is y = 320

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - - - - - -

Check fkor equation 1

x + y = 440

120 + 320 = 440

440 = 440

- - - - - - - -

Check for equation 2

2.5x + 5y = 1900

2.5(120) + 5(320) = 1900

300 + 1600 = 1900

1900 = 1900

- - - - - - - - - -

There were 120 Children at a cost of $ 300

There were 320 adults at a cost of $ 1600

- - - - - - - - - -

The solution set {120, 320 }

- - - - - - - - - -s-

Answer 3

1. a+c=440 (a is the number of adults, c is the number of children)
5a+2.5c=1900 ==> a+0.5c=380
==> 0.5c=60 ==> c=120 so the answer is (B)

2.substitue for each y in the 2nd eqution by 2x ==> 5x+2x=7
==> x=1 so the answer is (A) -I think you know that ordered pairs are written in (x,y) format-4

3. add both equtions together to elaminate the y term
==> 3x+5x=6+10 ==> x=2
subistuiute for x in eq. (1) ==> 3*2-2y=10 ==> -2y=4 ==> y=-2
the answer is (D)

Summary:
1.B
2.A
3.D

Answer 4

question 1
eqn 1
1900=5a+2.5c
eqn 2
a+c=440
a=440-c
sub eqn 2 into eqn 1
1900=5(440-c)+2.5
1900=2200-5c+2.5c
0=300-5c+2.5c
0=300-2.5c
2.5c=300
5c=600
c=120
you can work out adults by subbing into eqn 2
a+c=440
a+120=440
a=320

answer is b

question 2
eqn 1
y=2x
eqn 2
5x+y=7
sub eqn 1 into eqn 2
5x+2x=7
7x=7
x=1
sub into eqn 1
y=2x
y=2*1
y=2
i'd say solution a

question 3
eqn 1
3x-2y=10
eqn 2
5x+2y=6
add both eqns together
8x=16
x=2
sub in eqn 1
3x-2y=10
6-2y=10
-2y=4
y=-2

solution is d

Answer 5

let x= the no. of adults
y=the no. of children

x+y=440
5x+2.5y=1900

~>

-2.5x-2.5y=-1100
5x+2.50y=1900
----------------------
2.5x=800
x=800/2.5
=320

320+y=440
y=440-320
=120









y=2x
5x+y=7

5x=2x=7
7x=7
x=7/7
x=1

y=2(1)
y=2








3x-2y=10
5x+2y=6
-------------
8x=16
x=16/8
x=2

3(2)-2y=10
-2y=10-6
-2y=4
y=4/-2
y=-2

Answer 6

sorry i got to leave but the answer to the first question is B later