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

Question

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

(2 points)
___x +____ = ____

Answer 1

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 what Taylor read. Therefore, we can set up the equation as follows:

Half of the pages Taylor read is \( \frac{x}{2} \).

So, we can write:

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

To convert this into the form \( px + q = r \), we first eliminate the fraction by multiplying the entire equation by 2:

\[ x + 20 = 60 \]

Now, we can rewrite this in the desired format:

1. The coefficient of \( x \) is \( 1 \) (which is \( p \)).
2. The constant term on the left side is \( 20 \) (which is \( q \)).
3. The right side is \( 60 \) (which is \( r \)).

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

\[ 1x + 20 = 60 \]

Thus, the answer is:

___1____x +20 = 60.

Answer 2

So what’s the answer

Answer 3

The equation representing the problem, in the form \( px + q = r \), is:

1x + 20 = 60

So the specific numbers to fill in the blanks are:

___1____x + 20 = 60.

Answer 4

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 to represent this problem.

Answer 5

Let's break down the problem step by step and write the equation in the specified form \( px + q = r \).

1. Let \( x \) represent the number of pages Taylor read.

2. Half of the pages Taylor read is \( \frac{x}{2} \).

3. According to the problem, Arlene read 30 pages, which is 10 pages more than half of what Taylor read. Thus, we can express this relationship in an equation:

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

Next, we want to convert this equation into the form \( px + q = r \).

1. We can eliminate the fraction by multiplying the entire equation by 2:

   \[ 2 \left( \frac{x}{2} + 10 \right) = 2 \times 30 \]

   This simplifies to:

   \[ x + 20 = 60 \]

2. Now, we can rearrange the equation to the form \( px + q = r \):

   \[ 1x + 20 = 60 \]

Thus, the answer in the specified format \( px + q = r \) is:

1x + 20 = 60

So the specific numbers you would fill in the blanks with are:

___1____x + 20 = 60.

Answer 6

Don’t simplify it

Answer 7

Got it! Let's write the equation without simplifying the original relationship between Arlene's and Taylor's pages.

Starting point:

• Let \( x \) represent the number of pages Taylor read.
• According to the problem:
  • Half of the pages Taylor read is \( \frac{x}{2} \).
  • Arlene read 30 pages and that is 10 pages more than half of what Taylor read.

So, we can set up the equation directly from the problem statement:

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

Now, to express this in the form \( px + q = r \) without simplifying:

1. First, multiply both sides of the equation by 2 to eliminate the fraction:

\[ 2 \left(\frac{x}{2} + 10\right) = 2 \cdot 30 \]

This yields:

\[ x + 20 = 60 \]

2. But since you requested not to simplify this step, we can rearrange it to write it in the requested format without multiplying out:

To stay true to the original setup:

\[ x + 20 = 60 \quad \text{is equivalent to} \quad \frac{x}{2} + 10 - 30 = 0 \]

However, based on the request to not simplify, we will leave it as:

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

In order to fulfill your request to represent it without simplification, we can write the original equation in the form \( px + q = r \):

Equation in the form \( px + q = r \):

• Rewrite as: \[ x + 20 = 60 \]

However, without simplifying, directly from \( \frac{x}{2} + 10 = 30 \):

So it can be accurately stated as:

\(\frac{1}{2}x + 10 = 30\)

So for your request to fill that out appropriately, we can write:

___\(\frac{1}{2}\)__x + 10 = 30.

Please let me know if you'd like further clarification on this!

Answer 8

Cassandra measured her height as 63 inches. That is 6 inches less than 3 times her younger brother’s height. How tall is her younger brother?

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

Answer 9

Let's denote the height of Cassandra’s younger brother as \( x \).

According to the problem, Cassandra's height (63 inches) is 6 inches less than 3 times her brother’s height. This can be expressed with the following equation:

\[ 63 = 3x - 6 \]

Now, we want to rearrange this equation into the form \( px + q = r \).

1. First, we can add 6 to both sides of the equation:

\[ 63 + 6 = 3x \]

This simplifies to:

\[ 69 = 3x \]

2. Next, we will arrange to fit the format \( px + q = r \):

Rearranging gives:

\[ 3x - 69 = 0 \]

However, to reflect the format better, we can express it as:

\[ 3x - 69 = 0 \]

Thus, we identify:

• \( p = 3 \)
• \( q = -69 \)
• \( r = 0 \)

In summary, the equation in the form \( px + q = r \) representing this problem is:

3x - 69 = 0

So to fill in the blanks:

___3____x + -69 = 0.

If you would like to know the height of her younger brother as well, let me know!

Answer 10

The -69 and 0 is incorrect

Answer 11

I apologize for the oversight. Let's correctly express the equation in the form \( px + q = r \) based on the information provided without any confusion.

We know that:

• Cassandra's height (63 inches) is 6 inches less than 3 times her brother’s height (\(x\)).

From this statement, we can write the equation:

\[ 63 = 3x - 6 \]

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

1. First, add 6 to both sides:

\[ 63 + 6 = 3x \]

This simplifies to:

\[ 69 = 3x \]

Next, we can rearrange it into the desired form:

2. To express it as \( px + q = r \):

We can subtract 69 from both sides to bring it to the standard form:

\[ 3x - 69 = 0 \]

However, to ultimately fulfill your requirement of not overly complicating the answer, let’s retain the form with the original expressions.

So aiming for clarity:

Another way to write it directly from \( 63 \) being equal to \( 3x - 6 \):

1. Rearranging gives us:

   \[ 3x - 63 = 6 \]

So in the \( px + q = r \) format:

• \( p = 3 \)
• \( q = -63 \)
• \( r = 6 \)

Thus, the correct equation in the desired form is:

3x - 63 = 6

So filling in the blanks you'd have:

___3____x + -63 = 6.

Thank you for your patience! Let me know if you need more help.