Pleas help with these algebra questions?

Question

2. There were 1500 people at a high school football game. Student tickets were $2.00 and adult tickets were $3.50. The total receipts for the game were $3825. How many students bought tickets?

Let a = the number of adult tickets purchased.

Let s = the number of student tickets purchased.

a. Write a system of equations that can be used to determine the number of adult and student tickets purchased.

b. Determine the number of adults tickets sold and the number of student tickets sold. Use mathematics to explain how you determined your answer.

3. An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. Find the speed of the airplane in still air. This similar to the current problem as you have to consider the 25 mph tailwind and headwind

Let r = the rate or speed of the airplane in still air.

Let d = the distance

a. Write a system of equations for the airplane. One equation will be for the outbound trip with tailwind of 25 mph. The second equation will be for the return trip with headwind of 25 mph.

b. Solve the system of equations for the speed of the airplane in still air.

4. Your family likes to go to baseball games. At one game your family bought 5 soft drinks and 5 hot dogs for $22.25. At the next game your family attended they bought 4 soft drinks and 3 hot dogs for $14.50. What is the cost of one soft drink and one hot dog?

Let s = the cost of one soft drink

Let h = the cost of one hot dog

a. Write a system of equations modeling the situation described above.

b. Solve the system for the cost of one soft drink + one hot dog

Answer 1

Only know the 2 and 4.

2.

s + a = 1.500

s = 1.500 - a

2 * s + 3,5 * a  = 3.825

2* (1.500 - a ) + 3,5 * a = 3.825

3.000 - 2 * a + 3,5 * a = 3.825

3.000 + 1,5 * a = 3.825

1,5 * a = 825

a = 550

a + s = 1.500

s = 1.500 - a

s = 1.500 - 550

a = 950

4.

5s + 5h = 22,25 (multiply for 4)

4s + 3h = 14,50  (multiply for 5)

___________________________

20s + 20h = 89,00

20s + 15h = 72,50 (subtract 1st - 2nd equation )

________________________

5h = 16,5

h = 3,3 ( put h in one of the equations)

4s + 3h = 14,5

4s + 3*3,3 = 14,5

4s = 14,5 - 9,9

s = 1,15

EDIT :

3 problem  I am not sure if this is right.

v = velocity

v1= velocity wind

d = distance

t = time

v * t = d

we have to add the wind:

(v + v1)* t = d  

(v - v1)*t =d

d = d (distance is the same)

(v+v1)*t = (v-v1)*t

(v+25)*4 = (v-25)*5

4v + 100 = 5v -125

4v - 5v = -125 - 100

-v = -225 mph

v = 225 mph  ( speed in stil air)

(v+v1)*t = d

(225+25)*4 =d

250*4=d

d = 1000

(v-v1)*t=d

(225-25)*5=d

200*5= d

d = 1000

d = d

Answer 2

A+S=1500

$2.00+ $3.50=$3825

2(1500)3.5=$3825

105,000=$3825

Divide!

105,000/3825=$27.45(1500) =41,175 students?

Proportion

4/25= 5/X

4X=125

Divide!

X= 31.25mph

5s+5h= $22.25

4s+3h=$14.50

5(14.5)-(5)= $22.25

67.5/22.25= $3.08(5)= $22.25-$15.40=$6.85/5=$1.37

h=$3.08  

s=$1.37

Answer 3

Ok, so I did #2, and the following steps should help you complete the rest.

First, I wrote down the facts, 1500 people attended, Students cost $2, and adults cost $3.50.

I then wrote two equations based on the facts:

3.5a + 2s = $3825   <-- the coeffecients with the variables represent prices

a + s = 1500 <-- people who attended the game

I then set up the system of equations:

3.5a + 2s = 3825

    a  +  s = 1500

*it helps to line up the variables

Then I multiplied the bottom equation by 3.5, and ended up with:

3.5a + 2s = 3825

3.5a + 3.5s = 5250

Subtract the bottom equation from the top equation and the you end up with this:

1.5s = 1425

Then you divide 1425 by 1.5 and s will equal 950.  This number represents the number of students who attended the game.  Subtract 950 from 1500 and you will find the number of adults who attended the game.

Answer 4

answer 1 -

  adults+students=1500 people

so,

a+s= 1500..eq 1

total receipts were $3825

so,  

3.5a+2s=3825..eq 2

Solve the equations..

Multiplying eq 1 by 2

2a+2s=3000..eq 3

subtract eq 3 gby eq 2

   3.5a+2s=3825

  - 2a+2s=3000

  = 1.5a=825

so, a= 825/1.5 = 550

Put in eq 1

550+s=1500

so, s= 1500-550 = 950

so no. of adults were 550 and no. of students were 950

answer 3 -

5s+5h=22.25 ..eq1

4s+3h=14.5 ...eq2

multiply eq1 by 3 and eq 2 by 5

      15s+15h=66.75

     - 20s+15h=72.5

    = -5s= - 5.75

so, s= 1.15

Put value in eq 2..

4(1.15)+3h = 14.5

3h = 14.5 - 4.6 = 9.9

so, h= 9.9/3 = 3.3

so. cost one soft drink is 1.15$ and cost of one hot dog is 3.3$

one soft drink + one hot dog = 1.15+3.3 = 4.8 $

answer2...don't knw..sorry