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Question
Andrew is designing a house with an attached garage. He knows that the width of the house will be two times the width of the garage. There will also be a 6-foot-wide garden to the right of the house. The total width of the garage, house, and garden must be greater than 60 feet. How wide can the garage be? Solve this problem. Which graph most clearly communicates the solution? Note: You do not need to consider an upper limit for the width of the garage for this problem.(1 point)
Responses

A number line is labeled Possible Widths of Garage in Feet. The number line ranges from 0 to 28 in 1 unit increments. An open point is plotted at 18. A line extends from that point to the left, connecting to a closed point plotted at 0.
Image with alt text: A number line is labeled Possible Widths of Garage in Feet. The number line ranges from 0 to 28 in 1 unit increments. An open point is plotted at 18. A line extends from that point to the left, connecting to a closed point plotted at 0.

A number line ranges from 0 to 28 in 1 unit increments. A an open point is plotted at 18. A line extends from that point to the left and connects with a closed point plotted at 0.
Image with alt text: A number line ranges from 0 to 28 in 1 unit increments. A an open point is plotted at 18. A line extends from that point to the left and connects with a closed point plotted at 0.

A number line ranges from 0 to 28 in 1 unit increments. An open point is plotted at 18. A line extends from that point to the right and goes beyond 28.
Image with alt text: A number line ranges from 0 to 28 in 1 unit increments. An open point is plotted at 18. A line extends from that point to the right and goes beyond 28.

A number line is labeled Possible Widths of Garage in Feet. The number line ranges from 0 to 28 in 1 unit increments. An open point is plotted at 18. A line extends from that point to the right and goes beyond 28.

Answer 1

To solve the problem, let's define the variables and set up the equation based on the information given.

Let \( g \) be the width of the garage. According to the problem:
- The width of the house is \( 2g \) (twice the width of the garage).
- The width of the garden is 6 feet.

The total width of the garage, house, and garden can be expressed as:
\[
g + 2g + 6 = 3g + 6
\]
We know that this total must be greater than 60 feet:
\[
3g + 6 > 60
\]

Now, we can solve for \( g \):
1. Subtract 6 from both sides:
\[
3g > 54
\]
2. Divide both sides by 3:
\[
g > 18
\]

This indicates that the width of the garage must be greater than 18 feet.

Now, looking at the graph options provided:
- The solution \( g > 18 \) means that the values of \( g \) should be plotted on a number line starting from just after 18 and extending indefinitely to the right.

The correct graph that most clearly communicates this solution is:
**A number line ranges from 0 to 28 in 1 unit increments. An open point is plotted at 18. A line extends from that point to the right and goes beyond 28.**

This graph indicates that the width of the garage can be any value greater than 18.