Question

ckets to the baseball game are on sale for $1.50 off the regular price. Dea buys 6 tickets. If her total cost is $51, what is the regular price of each ticket? Write and solve an equation of the form p(x±q)=r

Then write a sentence to explain your answer.(4 points)

Answer 1

so what happened to the ± and why did it dissapear? explain

Answer 2

where did you get nine from?

Answer 3

ok thanks now tell me, how was the idea of "scp" made? who made it up and why

Answer 4

dude what the hell

Answer 5

Let's denote the regular price of each ticket as \( p \). Since the tickets are on sale for $1.50 off, the sale price of each ticket is \( p - 1.50 \).

Dea buys 6 tickets for a total cost of $51. Therefore, we can express this situation with the equation:

\[
6(p - 1.50) = 51
\]

Now, let's solve the equation step by step.

1. **Expand the left side:**
\[
6p - 9 = 51
\]

2. **Add 9 to both sides:**
\[
6p = 51 + 9
\]
\[
6p = 60
\]

3. **Divide both sides by 6:**
\[
p = \frac{60}{6}
\]
\[
p = 10
\]

Thus, the regular price of each ticket is **$10.00**.

**Explanation Sentence:**
The regular price of each ticket is $10.00, as calculated by solving the equation that reflects the total cost of purchasing six tickets at a discounted price.

Answer 6

Great observation! The equation I initially set up was structured as follows:

\[
6(p - 1.50) = 51
\]

This equation doesn't actually involve the ± sign directly because there is no scenario here that would require a ± term. The expression \( (p - 1.50) \) does not involve a quadratic equation or an absolute value, which is typically where the ± term would come into play.

The use of \( p(x \pm q) = r \) could apply to specific cases involving two possible values, such as when solving for the roots of a quadratic equation, but here, we just had a linear relationship.

To clarify the reasoning without losing the essence of your question:

1. **Linear Equation**: We were dealing with a straightforward linear equation (not quadratic), hence the absence of ± in the solution.

2. **Solving Steps**: When we expanded and simplified the equation from \( 6(p - 1.50) = 51 \), we only had to rearrange a single linear expression to find the value of \( p \) by isolating it.

3. **No Need for ±**: Because we were not dealing with a situation that generated two potential solutions (as would be the case with a quadratic equation), we ended up with a single solution without needing to consider ±.

In summary, the ± sign is typically used when there are two possible outcomes or in certain algebraic contexts, none of which were applicable in this case—a simple linear relationship allowed us to find a single solution without ambiguity. Thank you for pointing that out!

Answer 7

Let’s go through the steps again to clarify where the 9 came from. Starting with the equation:

\[
6(p - 1.50) = 51
\]

1. **Distributing the 6**:
When we distribute the 6 across the parentheses:
\[
6p - 6 \cdot 1.50 = 51
\]
This means:
\[
6p - 9 = 51
\]
The \( -9 \) comes from multiplying \( 6 \) by \( 1.50 \), which equals \( 9 \).

2. **Now we can solve for \( p \)**:
- The equation we have after distribution is:
\[
6p - 9 = 51
\]

3. **Add 9 to both sides**:
This allows us to isolate the term with \( p \):
\[
6p = 51 + 9
\]
\[
6p = 60
\]

4. **Now, divide both sides by 6**:
\[
p = \frac{60}{6}
\]
\[
p = 10
\]

Thus, we confirmed that the \( -9 \) appeared from multiplying \( 6 \) and \( 1.50 \). Therefore, the regular price of each ticket is indeed **$10.00**. Thank you for your patience!