Question

Question

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)
x
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 the pages Taylor read. We can express this relationship in an equation.

Half of the pages Taylor read is \( \frac{x}{2} \). If we add 10 to that, we should equal Arlene's 30 pages. Therefore, we can write the equation as:

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

To put it into the form \( px + q = r \), we'll first eliminate the fraction by multiplying the entire equation by 2:

\[ x + 20 = 60 \]

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

\[ 1x + 20 = 60 \]

Thus, the answer is: \[ x + 20 = 60 \]

Where \( p = 1 \), \( q = 20 \), and \( r = 60 \).

Answer 2

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
𝑝
𝑥
+
𝑞
=
𝑟
to represent this problem.

(2 points)
x
𝑥
+ =

Answer 3

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

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

\[ 63 = 3x - 6 \]

To convert it into the form \( px + q = r \), we can rearrange the equation. First, we'll add 6 to both sides:

\[ 63 + 6 = 3x \] \[ 69 = 3x \]

Now, we can write it in the required form:

\[ 3x - 69 = 0 \]

To be consistent with the requested form \( px + q = r \), we can rewrite it as:

\[ 3x + 0 = 69 \]

So the final result can be written as:

\[ 3x + 0 = 69 \]

Where \( p = 3 \), \( q = 0 \), and \( r = 69 \).

Answer 4

wrong

Answer 5

I apologize for the confusion in my response. Let me clarify the situation and set up the correct equation.

Given the problem:

Cassandra's height is 63 inches, which is 6 inches less than 3 times her younger brother's height.

We can start by setting:

• Let \( x \) be the height of Cassandra's younger brother.

The relationship described in the problem can be written as:

\[ 63 = 3x - 6 \]

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

First, we’ll add 6 to both sides:

\[ 63 + 6 = 3x \] \[ 69 = 3x \]

Next, we can write this in the form \( 3x = 69 \). To fit it into the structure \( px + q = r \), we can adjust this:

\[ 3x - 69 = 0 \]

However, to clearly denote it in the required format, we can express it as:

\[ 3x + 0 = 69 \]

So, the equation in the form \( px + q = r \) can be written as:

\[ 3x + 0 = 69 \]

Where:

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

I appreciate your patience, and thank you for bringing this to my attention!

Answer 6

0 and 69 are wrong, 3x+_=_?

Answer 7

Apologies for the confusion in the earlier responses. Let's set up the correct equation based on the problem statement accurately.

We know:

• Cassandra's height: \( 63 \) inches
• This is \( 6 \) inches less than \( 3 \) times her younger brother's height.

So we can express this relationship as:

\[ 63 = 3x - 6 \]

To rewrite it in the form \( px + q = r \):

1. Add \( 6 \) to both sides:

\[ 63 + 6 = 3x \] \[ 69 = 3x \]

2. Rearranging this to fit \( px + q = r \), we can subtract \( 69 \) from both sides:

\[ 3x - 69 = 0 \]

However, to express it specifically in the form \( px + q = r \):

We can rewrite it as:

\[ 3x - 69 = 0 \quad \text{or} \quad 3x + 0 = 69 \]

If we strictly follow the structure \( px + q = r \) without using \( 0 \):

Starting from \( 3x = 69 \):

Let's look for a proper adjustment to meet your request where \( q \) can be any non-zero number in the equation.

So if we express it as:

\[ 3x + 0 = 69 \]

Now, to provide it in the requested format specifically:

\[ 3x - 69 = 0 \]

is also acceptable.

To fit your query specifically towards

\( 3x + 6 = 69 \)

if we misplaced or misunderstood:

The equation:

\[ 3x - 6 = 63 \]

is observably simpler for expression as:

\[ 3x + (-6) = 63 \]

To reflect \( px + q = r\) format:

Therefore, directly expressing for clarity:

\[ 3x + (-6) = 63 \]

Where \( p = 3 \), \( q = -6 \), \( r = 63 \).

Would be an ideal correction. Thank you for your understanding, and I hope this clarity meets your requirements!

Answer 8

Anthony got a job babysitting. Each hour he works he will be paid $8.00. As a bonus, he will earn an additional $1.50 per hour for each child he watches. If his total hourly rate is $12.50, how many children does he watch?

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

(2 points)
x
𝑥
+ =

Answer 9

Let \( x \) represent the number of children Anthony watches.

Anthony's total earnings per hour can be expressed as the sum of his hourly rate and the bonus he receives for watching children.

His base pay is $8.00 per hour, and he earns an additional $1.50 per hour for each child. Therefore, his total pay per hour can be expressed as:

\[ \text{Total Pay} = 8 + 1.5x \]

According to the problem, this total pay is $12.50 per hour. We can set up the equation:

\[ 8 + 1.5x = 12.50 \]

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

1. Subtract \( 8 \) from both sides:

\[ 1.5x = 12.50 - 8 \]

2. Calculate \( 12.50 - 8 \):

\[ 1.5x = 4.50 \]

Now we can express this equation in the requested form:

\[ 1.5x - 4.5 = 0 \]

Or, if we want to express it as:

\[ 1.5x + (-4.5) = 0 \]

Thus, the final result for the equation is:

\[ 1.5x - 4.5 = 0 \]

So, in the format you requested:

\[ 1.5x + (-4.5) = 0 \]

Where \( p = 1.5 \), \( q = -4.5 \), and \( r = 0 \).

Alternatively, to format it as you wanted it:

\[ 1.5x + 0 = 4.50 \]

Would yield another useful \( p, q, r \) form. Thank you for your attention, and let me know if you have more questions!

Answer 10

wrong read the queston again

Answer 11

I apologize for the oversight. Let’s carefully analyze the problem and set it up correctly.

Given:

• Anthony earns $8.00 per hour as a base pay.
• He earns an additional $1.50 per hour for each child he watches.
• His total hourly rate is $12.50.

Let \( x \) represent the number of children he watches.

The total hourly pay can be expressed as:

\[ \text{Total Pay} = \text{Base Pay} + \text{Bonus Pay} \] \[ \text{Total Pay} = 8 + 1.5x \]

According to the problem, this total pay is equal to $12.50:

\[ 8 + 1.5x = 12.50 \]

Now, we need to rearrange this equation to fit the format \( px + q = r \).

1. Subtract 8 from both sides:

\[ 1.5x = 12.50 - 8 \] \[ 1.5x = 4.50 \]

Now rearranging further gives us:

\[ 1.5x - 4.50 = 0 \]

However, to express it in the desired form:

\[ 1.5x + (-4.50) = 0 \]

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

\[ 1.5x - 4.50 = 0 \]

To neatly put into the format \( px + q = r \):

\[ 1.5x + 0 = 4.50 \]

So the answer following your requested format \( px + q = r \):

\[ 1.5x + 0 = 4.50 \]

Where:

• \( p = 1.5 \)
• \( q = 0 \)
• \( r = 4.50 \)

Again, I appreciate your patience, and thank you for pointing out the error! Please let me know if else you need assistance with.