I need math help! Please help!?

Question

I had to do ten of these problems for homework, but I'm stumped on this one. I also need to write an equation to show my work. If you can help, it would be greatly appreicated!

Carmen sold play tickets. Each adult ticket cost $4.00 and each student ticket cost $2.00. The total number of tickets sold was 260, and the total income was $700.00. How many of each kind of ticket were sold?

Please help me find and answer. Thanks!

Answer 1

This is just linear algebra...

Let A=the number of adult tickets, and S = the number of student tickets. Then, we have two equations:

A + S = 260

4A + 2S = 700

Using equation 1, if we let A = 260 - S, then substitute this into equation 2:

4(260 - S) + 2S = 700

4*260 - 2S = 700

S = (4*260 - 700)/2 = 170

Now, back substituting into equation 1:

A = 260 - S = 260 - 170 = 90

FINAL ANSWERS:

Adult Tickets: 90
Student Tickets: 170

Hope that helps! :)

Answer 2

With one variable: let a be the number of adult tickets. Then 260 - a =the number of kids tickets. 4a + 2(260-a) = 700
Multiply out and solve for a, then subtract from 260 to get the number of student tickets.

With two variables: let a = number of adult tickets and s = number of student tickets. Then

a + s = 260
4a + 2s = 700

Multiply all the terms in the first equation by -2 and add them to the second. This eliminates s.

-2a - 2s = -520
4a + 2s = 700

becomes when you add them

2a =180

Solve for a then subtract it from 260 to get s.

Answer 3

A = # of adult tickets
S = # of student tickets

1) A + S = 260

2) 4A + 2S = 700

Solve equation 1 for A and substitute into equation 2

A = 260 - S

4(260 - S) + 2S = 700
1040 - 4S + 2S = 700
- 2S = - 340
S = 170

A = 260 - 170
A = 90

Check

4(90) + 2(170) = 700
360 + 340 = 700
700 = 700

Answer 4

I'll use adult tickets as "a" & student tickets as "s"

1. Total income is represented as 4a+2s = 700, meaning the adult ticket income plus student ticket income equals 700.
2. Total tickets is represented as a+s = 260, meaning the number of adult tickets plus number of student tickets equals 260
3. You have to solve for one letter to find the value. So let's solve for "s"
4. a+s=260. To solve for "s", you subtract "a" on both sides. You end up with s=260-a. Use this to solve the total income.
5. 4a+2s=700. Substitute for "s". 4a+2(260-a)=700. Since s=260-a.
6. Multiply & factor out. 4a+520-2a=700.
7. 2a=180
8. a=90. Meaning, there are 90 adult tickets.
9. Since there are 90 adult tickets & 260 total tickets, there are 170 student tickets.

Answer is 90 adult tickets & 170 student tickets.

Answer 5

x=90 y= 170 it is simultanoeous equation the two equation are
x+y=260 and 4x+2y=700