Question

In the equations below, a is the price, in dollars, of an adult ticket to a school play, and s is the price of a student ticket.5a+3s=42and3a+s=22

What is the price of an adult ticket to the play?

a) $8
b) $10
c) $12
d) $14

Answer 1

The system of equations 5a + 3s = 42 and 3a + s = 22 should be solved for 'a' representing the price in dollars of an adult ticket. However, the calculated answer of $6 does not match the provided options of $8, $10, $12, or $14, indicating a possible mistake in the question or calculations.

Step-by-step explanation:

We are given two equations: 5a + 3s = 42 and 3a + s = 22. To find the price of an adult ticket, we need to solve this system of linear equations for 'a', which represents the price in dollars of an adult ticket.

Let's use the substitution or elimination method to solve the system:

1. Multiply the second equation by 3 to make the coefficients of 's' equal:
   3(3a + s) = 3(22)
   9a + 3s = 66
2. Now we have a new system:
   5a + 3s = 42 (equation 1)
   9a + 3s = 66 (equation 2)
3. Subtract equation 1 from equation 2:
   (9a + 3s) - (5a + 3s) = 66 - 42
   4a = 24
4. Divide both sides by 4 to solve for 'a':
   a = 24 / 4
   a = 6

However, these calculations do not seem to lead to any of the provided multiple-choice options (a) $8, (b) $10, (c) $12, (d) $14. It appears there may have been an error in the calculations. Please note that the price calculated here does not match with given options, so the question may need to be revisited to ensure the provided equations and options are accurate.