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MATH / Tina the tourist goes on a trip. She starts at the origin and drives north (in…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Tina the tourist goes on a trip. She starts at the origin and drives north (in the positive yy direction) for 1010 units. Then she turns east (the positive xx direction) and as she's turning her camera flies out the window and lands exactly at (0,10)(0,10). She then drives 99 units east, turns and drives 88 units north. She continues this pattern of turning and driving one unit less than after the previous turn, until stopping after driving 11 unit east. She reaches for her camera only to find it missing! She activates the GPS homing device on her camera and drives back to it in a straight line. What is the equation of this line? Express your answer as ax+by=cax+by=c, where aa, bb, and cc are integers, a>0a>0, and aa is as small as possible.
Plain-text mathematical notation (without MathML)
Tina the tourist goes on a trip. She starts at the origin and drives north (in the positive y direction) for 10 units. Then she turns east (the positive x direction) and as she's turning her camera flies out the window and lands exactly at (0,10). She then drives 9 units east, turns and drives 8 units north.  She continues this pattern of turning and driving one unit less than after the previous turn, until stopping after driving 1 unit east. She reaches for her camera only to find it missing! She activates the GPS homing device on her camera and drives back to it in a straight line. What is the equation of this line? Express your answer as ax+by=c, where a, b, and c are integers, a>0, and a is as small as possible.
Original LaTeX notation
Tina the tourist goes on a trip. She starts at the origin and drives north (in the positive $y$ direction) for $10$ units. Then she turns east (the positive $x$ direction) and as she's turning her camera flies out the window and lands exactly at $(0,10)$. She then drives $9$ units east, turns and drives $8$ units north.  She continues this pattern of turning and driving one unit less than after the previous turn, until stopping after driving $1$ unit east. She reaches for her camera only to find it missing! She activates the GPS homing device on her camera and drives back to it in a straight line. What is the equation of this line? Express your answer as $ax+by=c$, where $a$, $b$, and $c$ are integers, $a>0$, and $a$ is as small as possible.

level

Level 5

type

Algebra

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Source and history

task_id
a97aeec4-deb4-502f-914b-e8877e885003
task_key
algebra--test--a97aeec4-deb4-502f-914b-e8877e885003
task_revision_id
1
config / split
algebra / test

Official source

initial import