Question

Josie currently has $13 and plans to save an additional $7 each week to buy a jacket. She made a table showing the total amount of money she will have saved for different weeks.

Number of weeks 0 3 5 7
Total amount of money ($) 13 34 48 62
Which equation represents the relationship between the number of weeks, x, and the total amount of money, y, Josie will have saved?

Responses

x + 7y = 13
x + 7 y = 13

7x−y=−13
7 x minus y equals negative 13

x−7y=13
x minus 7 y equals 13

7x + y = 13

Answer 1

To find the equation that represents the relationship between the number of weeks \( x \) and the total amount of money \( y \) that Josie will have saved, we start by noting the information given:

- Josie currently has $13.
- She saves an additional $7 each week.

From this, we can determine that after \( x \) weeks, she will have saved:

\[
y = 13 + 7x
\]

This equation can be rearranged to fit a standard linear form. If we move \( y \) to one side:

\[
y - 7x = 13
\]

Now, rewriting this gives us:

\[
-7x + y = 13
\]

If we multiply through by -1 to make the coefficient of \( x \) positive, we have:

\[
7x - y = -13
\]

Therefore, the correct equation representing the relationship between the number of weeks \( x \) and the total amount of money \( y \) Josie will have saved is:

**7x - y = -13**