Shawn has a budget of $50 per month to spend on bus fare. He made a table showing the total amount of bus money he will have left after the given number of rides.

Question

Number of rides 0 9 18 27
Total amount of bus money left ($) 50 41 32 23
Which equation, in standard form, represents the relationship between the number of bus rides, x, and the amount of bus money Shawn will have left, y?

50y = x
50 y = x

50x = y
50 x = y

x + y = 50
x + y = 50

50x + 50y = 1

Answer 1

To find the equation that represents the relationship between the number of bus rides (\(x\)) and the amount of bus money Shawn will have left (\(y\)), we can analyze the data provided.

1. Identify the total budget and the cost per ride.

   • Shawn has a budget of $50.
   • We can calculate how much money he has left after a certain number of rides.

2. Calculate the cost per ride.

   • From the table:
     • After 9 rides, he has $41 left, indicating he spent $9 (since \(50 - 41 = 9\)).
     • Therefore, the cost per ride is \( \frac{9}{9} = 1 \) dollar.
   • Checking other values:
     • After 18 rides, he spent \(50 - 32 = 18\) dollars.
     • After 27 rides, he spent \(50 - 23 = 27\) dollars.

3. Determine the relationship.

   • Each ride costs $1. Therefore, for \(x\) rides, he spends \(x\) dollars.
   • The amount left after \(x\) rides is given by \(50 - x\).

So, the relationship is:

\[ y = 50 - x \]

4. Convert to standard form.

   • Rearranging \(y = 50 - x\) gives us: \[ x + y = 50 \]

5. Conclusion. The standard form of the equation that represents the relationship is:

\(x + y = 50\).