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Arlene read 30 pages that Is 10 pages more than half of the pages Taylor read. How many pages did Taylor read?

Write and equation in the for px+q=r to represent this problem

3 answers

Let's denote the number of pages Taylor read as \( x \).

According to the problem, Arlene read 30 pages, which is 10 pages more than half of the pages Taylor read. We can express this relationship mathematically.

First, half of the pages Taylor read is \(\frac{x}{2}\). Since Arlene read 10 pages more than this, we can write the equation as:

\[ \frac{x}{2} + 10 = 30 \]

To put this equation in the form \( px + q = r \), we can start by simplifying.

  1. Subtract 10 from both sides: \[ \frac{x}{2} = 20 \]

  2. Multiply both sides by 2 to eliminate the fraction: \[ x = 40 \]

Now rewrite the original equation in the required form \( px + q = r \):

From the equation \(\frac{x}{2} + 10 = 30\):

If we multiply through by 2 to eliminate the fraction: \[ x + 20 = 60 \]

In the \( px + q = r \) form, this can be expressed as: \[ 1x + 20 = 60 \]

So, the values of \( p \), \( q \), and \( r \) are:

  • \( p = 1 \)
  • \( q = 20 \)
  • \( r = 60 \)

Thus, the equation representing this problem is: \[ x + 20 = 60 \]

And Taylor read \( 40 \) pages.

Wrong

I apologize for any confusion earlier. Let's carefully analyze the problem again and formulate the equation correctly.

Given:

  • Arlene read 30 pages, which is 10 pages more than half of the pages Taylor read.

Let's denote the number of pages Taylor read as \( x \).

According to the problem, we have the relationship:

\[ 30 = \frac{x}{2} + 10 \]

Now, we'll rewrite this equation in the form \( px + q = r \):

  1. Start with the original equation: \[ 30 = \frac{x}{2} + 10 \]

  2. Subtract 10 from both sides: \[ 30 - 10 = \frac{x}{2} \] Which simplifies to: \[ 20 = \frac{x}{2} \]

  3. Now, multiply both sides by 2 to eliminate the fraction: \[ 40 = x \]

So, Taylor read \( 40 \) pages.

To express this in the form \( px + q = r \), we can rewrite the equation we started with:

From: \[ 30 - 10 = \frac{x}{2} \] We can multiply by 2: \[ 20 \times 2 = x \quad \text{(which simplifies to already get } x = 40) \]

Therefore, the equation in \( px + q = r \) form is: \[ x - 40 = 0 \]

Or rearranging, we can say: \[ 1x + 0 = 40 \]

So we could also express it as: \[ x - 40 = 0 \]

Summary:

Taylor read 40 pages. The equation representing this in \( px + q = r \) form is: \[ 1x + 0 = 40 \] Thank you for your patience, and I appreciate the opportunity to clarify this for you!