Question

Madison lives between Anoa and Jamie. The distance between Anoa and Madison's house are represented by 3x+2 miles, the distance between Madison and Jamie's house is represented by 3x+4, and the distance between Anoa and Jamie's house is represented by 9x-3 miles. Find the value of x. Then find the distance between Madison's house and Jamie's house.

Answer 1

To find the value of \( x \), we can set up an equation based on the relationship between the distances. The total distance from Anoa to Jamie can be expressed as:

\[
\text{Distance from Anoa to Madison} + \text{Distance from Madison to Jamie} = \text{Distance from Anoa to Jamie}
\]

Substituting the given distances:

\[
(3x + 2) + (3x + 4) = 9x - 3
\]

Combining the distances on the left side:

\[
3x + 2 + 3x + 4 = 9x - 3
\]
\[
6x + 6 = 9x - 3
\]

Next, we solve for \( x \) by isolating \( x \):

1. Subtract \( 6x \) from both sides:

\[
6 = 3x - 3
\]

2. Next, add \( 3 \) to both sides:

\[
9 = 3x
\]

3. Divide both sides by \( 3 \):

\[
x = 3
\]

Now that we have found \( x \), we can find the distance between Madison's house and Jamie's house. The distance is represented by:

\[
3x + 4
\]

Substituting \( x = 3 \):

\[
3(3) + 4 = 9 + 4 = 13
\]

Therefore, the value of \( x \) is \( 3 \) and the distance between Madison's house and Jamie's house is \( 13 \) miles.

In summary,
\[
x = 3 \quad \text{and the distance between Madison's house and Jamie's house is } 13 \text{ miles.}
\]