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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)

7 answers

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.

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

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!

where did you get nine from?

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!

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