Solve the system of equations.

Question

Ndiba's school is selling tickets at a fall musical. On the first day of ticket sales the school sold 11 adult tickets and 2 child tickets for a total of $151. The school took in $271 on the second day by selling 11 adult tickets and 10 child tickets. What is the price each of one adult ticket and one child ticket?

A) adult ticket: $11,

child ticket: $15

B) adult ticket: $13,

child ticket: $9

C) adult ticket: $15,

child ticket: $11

D )adult ticket: $9,

child ticket: $6

Answer 1

Let's set a = adult tickets and c = child tickets.

That would make:

11a + 2c = 151

11a + 10c = 271

There are two ways of solving this:

1. Set the equations equal to each other. Notice how both equations have 11a in them. To make it easy, let's set each equation equal to 11a. We get 11a = 151 - 2c and 11a = 271 - 10c.
2. Since 11a is equal to 11a, set 151 - 2c = 271 - 10c
3. Now solve for c.
4. 8c = 120
5. c = 15
6. Plug c back into one of the equations to find a.
7. 11a + 2(15) = 151
8. 11a + 30 = 151
9. 11a = 121
10. a = 11
11. Since both times the school sold 11 adult tickets, the only difference is 8 child tickets and $120. Therefore 8c = 120.
12. c = 15
13. Plug c back in to find a
14. 11a + 10(15) = 271
15. 11a + 150 = 271
16. 11a = 121
17. a = 11

The answer is A. Each adult ticket costs $11, and each child ticket costs $15.

Answer 2

We have 2 unknowns to solve for, therefore, we need 2 equations.

Let A = price of adult ticket

C = price of a child ticket

Eq. 1: 11A + 2C = $151

Eq. 2: 11A + 10C = $271

If we subtract Eq. 1 from Eq. 2 we can solve for "C":

11A + 10C = 271 Eq. 2

-(11A + 2C = 151) Eq. 1

8C = 120

(8C)/8 = 120/8 Divide both sides by 8

C = 15 Result for "C"

Using this value for "C" in either the first or second equation, we can solve for "A":

11A + 2C = 151 Eq.1

11A = 151 - 2C Subtract 2C from both sides

11A = 151 - 2(15) Substitute 15 for "C"

11A = 151 - 30 Multiply 2 X 15

11A = 121 Simplify

11A/11 = 121/11 Divide both sides by 11

A = 11 Result for "A"

Our answer is adult tickets sold for $11 and children tickets sold for $15, which is answer A.

Hope this helps!