Question

Maureen proposes giving each student two free tickets to the fair, with the price represented by 2(x – 2) + 5. Liam proposes giving students free admission, with the price represented by 2x. What number of tickets would result in the same price for each student under either proposal? Explain.

Answer 1

Maureen and Liam propose different pricing models for fair tickets. When setting their expressions equal to each other and solving for x, we find that there is no number of tickets that would result in the same price for each student under either proposal.

Step-by-step explanation:

Maureen proposes giving each student two free tickets to the fair, with the price represented by 2(x – 2) + 5. Liam proposes giving students free admission, with the price represented by 2x. To find the number of tickets that would result in the same price for each student under either proposal, we need to equate the two expressions and solve for x:

1. Set the two expressions equal to each other: 2(x – 2) + 5 = 2x.
2. Distribute the 2 on the left side: 2x – 4 + 5 = 2x.
3. Combine like terms: 2x + 1 = 2x.
4. Subtract 2x from both sides: 1 = 0.

Therefore, there is no number of tickets that would result in the same price for each student under either proposal. The equations are not equivalent and do not have a common solution.

Answer 2

Not solvable with the data given

Step-by-step explanation:

Part 1: 2 (x - 2) + 5

Part 2: 2x

So, Part 1 = Part 2

2 (x - 2) + 5 = 2x

Distribute

2x - 4 +5 = 2x

Add

-4 + 5 = 1

You now have: 2x + 1 = 2x

Divide

2x 1 = 2x

2x 2x 2x

x + 1 = x

2x

This will never be equal or be solvable. As it is not solvable, there is no number of tickets that will equal the same price for each student. Even if you use 1 for the x, they will not equal. If you try it on a graph at no point do they intersect at the same point.

For example, using 1.

2 (x -2) + 5

2 (1 - 2) + 5

2 (-1) + 5

2 - 4 + 5

- 2 + 5

3

2x

2(1)

2