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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 an equation in the form px+q=r
𝑝
𝑥
+
𝑞
=
𝑟
to represent this problem.

(2 points)
blank x+ blank = blank

3 answers

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

According to the problem, half of the pages Taylor read is \( \frac{x}{2} \). The problem states that Arlene read 30 pages, which is 10 pages more than half of what Taylor read. Therefore, we can set up the equation as follows:

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

Now to convert this into the form \( px + q = r \):

  1. Start by isolating \( \frac{x}{2} \): \[ 30 - 10 = \frac{x}{2} \ 20 = \frac{x}{2} \]

  2. Multiply both sides by 2 to eliminate the fraction: \[ 2 \times 20 = x \ 40 = x \]

So, Taylor read 40 pages.

Now rewriting the original equation to fit \( px + q = r \):

Starting with \( 30 = \frac{x}{2} + 10 \), we can rearrange it to make it match the desired format.

Multiply the entire equation by 2 to eliminate the fraction: \[ 60 = x + 20 \ x - 60 + 20 = 0 \ x - 40 = 0 \]

The final equation in the form \( px + q = r \) is:

\[ 1 x - 40 = 0 \]

To fit your blanks:

  • blank \( p \) = 1
  • blank \( x \) = \( x \)
  • blank \( q \) = -40
  • blank \( r \) = 0

So, the formatted equation is:

1x - 40 = 0

wrong give me the right answer

Apologies for the confusion in my previous response. Let's set up the correct equation from the beginning.

Arlene read 30 pages, which is described as 10 pages more than half of what Taylor read. We denote the number of pages Taylor read as \( x \).

According to the statement, we can express this mathematically as:

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

Now, to put this into the form \( px + q = r \):

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

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

  3. Multiply both sides by 2 to eliminate the fraction: \[ 2 \times 20 = x \ 40 = x \]

Now, if we want to write the equation in the form \( px + q = r \): Starting from \( 20 = \frac{x}{2} \):

Multiply by 2: \[ 40 = x \]

Rearrange it to \( x - 40 = 0 \):

In the form \( px + q = r\):

  1. Replace \( p \) with 1 (the coefficient of \( x \)).
  2. \( q \) will be -40 (subtracting 40 from both sides).
  3. \( r \) will be 0 (the result of rearranging).

The final equation is:

1x - 40 = 0

So filling in your blanks:

\[ \text{1x} + \text{(-40)} = \text{0} \]

Thank you for your patience, and I hope this clarifies the problem correctly! Taylor read 40 pages.