Aaron has a budget of $100 per month to spend on lunch. He made a table showing the total amount of lunch money he will have left after the given number of lunches.

Question

Number of lunches 0 5 10 15
Total amount of lunch money left ($) 100 75 50 25
Which equation, in standard form, represents the relationship between the number of lunches, x, and the amount of lunch money Aaron will have left, y?

Responses

x + 5y = 100
x + 5 y = 100

100x + y = 5
100 x + y = 5

x + 100y = 5
x + 100 y = 5

5x + y = 100

Answer 1

To find the equation that represents the relationship between the number of lunches (x) and the amount of lunch money left (y), we can look at the table values.

From the table:

• When \( x = 0 \), \( y = 100 \)
• When \( x = 5 \), \( y = 75 \)
• When \( x = 10 \), \( y = 50 \)
• When \( x = 15 \), \( y = 25 \)

The amount of money spent increases by $25 for every 5 lunches:

• From 0 to 5 lunches, money decreased from $100 to $75 (a decrease of $25).
• From 5 to 10 lunches, money decreased from $75 to $50 (a decrease of $25).
• From 10 to 15 lunches, money decreased from $50 to $25 (a decrease of $25).

Thus, the amount spent per lunch is:

\[ \text{Amount spent per lunch} = \frac{25}{5} = 5 \]

This means if Aaron has \( y \) dollars left, then for every lunch (x), he spends $5, which leads to the equation:

\[ y = 100 - 5x \]

To rewrite this in standard form (Ax + By = C), we can rearrange the equation:

\[ 5x + y = 100 \]

Thus, the correct response is:

5x + y = 100