This trail sign is on the northside of the Rio Salado near the Central Avenue parking lot in Phoenix, Arizona.

The trail sign says...

```   +-------------------------------+
|  Central Avenue Gateway to:   |
| 7th Street Bridge   0.5 miles |
| 16th Street Bridge  1.4 miles |
+-------------------------------+
```

[side-bar] In the above trail sign, should 0.5 miles be 0.5 mile? And, should 1.4 miles be 1.4 mile?

To help when it comes to doing BARS (Basic Arithmetic Road Signs), MathBabbler has memorized the following equation.

```   (1 + sqrt(5))/2 = Phi
```

Let's do the math...

```   the numbers are:  7  0.5  16  1.4

the Phi math is:  0.5 + sqrt(floor(7 - 1.4) / sqrt(16)) = Phi

observe...
Phi golden ratio = 1.61803399
7 - 1.4 = 5.6
floor(5.6) = 5
sqrt(16) = 4
sqrt(5/4) = sqrt(5)/sqrt(4) = sqrt(5)/2
0.5 = 1/2
1/2 + sqrt(5)/2 = (1 + sqrt(5))/2

more math:  ceil(1.4 / 0.5) = sqrt(16 - 7)

observe...
1.4 / 0.5 = 2.8
ceil(2.8) = 3
16 - 7 = 9
sqrt(9) = 3

more math:  ceil(1.4 / 0.5) = 7 - sqrt(16)
```

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 24 December 2007
The text passage contains a trail sign with distances and a series of mathematical equations and observations related to the numbers on the sign.
multiple_questions_with_answers

the passage includes multiple mathematical questions or observations, and answers or solutions are provided for each of them.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
This trail sign is on the northside of the Rio Salado near the Central Avenue parking lot in Phoenix, Arizona.

The trail sign says...

```   +-------------------------------+
|  Central Avenue Gateway to:   |
| 7th Street Bridge   0.5 miles |
| 16th Street Bridge  1.4 miles |
+-------------------------------+
```

[side-bar] In the above trail sign, should 0.5 miles be 0.5 mile? And, should 1.4 miles be 1.4 mile?

To help when it comes to doing BARS (Basic Arithmetic Road Signs), MathBabbler has memorized the following equation.

```   (1 + sqrt(5))/2 = Phi
```

Let's do the math...

```   the numbers are:  7  0.5  16  1.4

the Phi math is:  0.5 + sqrt(floor(7 - 1.4) / sqrt(16)) = Phi

observe...
Phi golden ratio = 1.61803399
7 - 1.4 = 5.6
floor(5.6) = 5
sqrt(16) = 4
sqrt(5/4) = sqrt(5)/sqrt(4) = sqrt(5)/2
0.5 = 1/2
1/2 + sqrt(5)/2 = (1 + sqrt(5))/2

more math:  ceil(1.4 / 0.5) = sqrt(16 - 7)

observe...
1.4 / 0.5 = 2.8
ceil(2.8) = 3
16 - 7 = 9
sqrt(9) = 3

more math:  ceil(1.4 / 0.5) = 7 - sqrt(16)
```

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 24 December 2007
user
The text passage contains a trail sign with distances and a series of mathematical equations and observations related to the numbers on the sign.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS

The passage includes multiple mathematical questions or observations, and answers or solutions are provided for each of them.