Algebra homework

Question

Alice’s school is selling tickets to the school carnival. On the first day of ticket sales, the school sold 3 adult tickets and 9 student tickets for a total of $75. The second day, the school sold $67 by selling 8 adult and 5 student tickets. What is the price of each of one adult and one student ticket ?

Answer 1

Let's let the cost of one student ticket be represented by the variable s and the cost of one adult ticket be represented by the variable a.

We can create two equations with two unknowns using the information in the problem:

3a + 9s = 75

8a + 5s = 67

Now we can solve these equations using elimination. Multiply the first equation by -5 and the second equation by 9:

-15a - 45s = -375

72a + 45s = 603

Now combine these two equations as follows:

-15a - 45s = -375

72a + 45s = 603

57a = 228

a = 228/57

a = $4 The cost of an adult ticket will be $4

Since 3a + 9s = 75, we can substitute 4 for a and solve for the cost of one student ticket, s:

3*4 + 9s = 75

12 + 9s = 75

12 + 9s -12 = 75 -12

9s = 63

9s/9 = 63/9

s = $7

The cost of one student ticket is $7.