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(a) B

(b) $2

Step-by-step explanation:

(a) Let's say the cost of a ticket is t and the cost of popcorn is p. Then we can write the two equations from the table:

12t + 8p = 184

9t + 6p = 138

We need to solve this, so let's use elimination. Multiply the first equation by 3 and the second equation by 4:

3 * (12t + 8p = 184)

4 * (9t + 6p = 138)

We get:

36t + 24p = 552

36t + 24p = 552

Subtract the second from the first:

    36t + 24p = 552

-    36t + 24p = 552

       0 = 0

Since we get down to 0 = 0, which is always true, we know that we cannot determine the cost of each ticket because there is more than one solution (infinitely many, actually). The answer is B.

(b) Our equation from this, if we still use t and p, is:

5t + 4p = 82

Now, just choose any of the two equations from above. Let's just pick 9t + 6p = 138. Now, we have the system:

5t + 4p = 82

9t + 6p = 138

To solve, let's use elimination again. Multiply the first equation by 6 and the second one by 4:

6 * (5t + 4p = 82)

4 * (9t + 6p = 138)

We get:

30t + 24p = 492

36t + 24p = 552

Subtract the second from the first:

    36t + 24p = 552

-    30t + 24p = 492

      6t + 0p = 60

So, t = 60/6 = $10. Plug this back into any of the equations to solve for p:

5t + 4p = 82

5 * 10 + 4p = 82

50 + 4p = 82

4p = 32

p = 32/4 = $8

So the ticket costs 10 - 8 = $2 more dollars than the popcorn.

B. No, the corresponding system of equations has multiple solutions; $2

Step-by-step explanation:

a) B. No, the corresponding system of equations has multiple solutions

Set up a system of equations where x = ticket cost, and y = popcorn.

The equations would be:

12x + 8y = 184 and 9x + 6y = 138

There would be no solution, because the first equation is the 2nd equation multiplied by 4/3.

b) Set up a system of equations, where x = ticket cost, and y = popcorn. The equation would be 5x + 4y = 82, and another equation would be 12x + 8y = 184 (taken from previous part). You multiply " 5x + 4y = 82" by 2, and get 10x + 8y = 164 and subtract it from the other equation, to get 2x = 20, which makes x = 10, and y = 8. That makes a ticket cost $2 more than a popcorn

y > 1/3x

y < = -x + 4

hope this : )