Question

At an arcade, tokens are stored in rolls. Each roll contains 40 tokens. A player uses 8 tokens from 1 roll. Which function shows the relationship between y, the total number of tokens remaining, and x, the number of rolls?

a) y = 40x - 8
b) y = 40x + 8
c) y = 8x - 40
d) y = 8x + 40

Answer 1

The correct function representing the relationship between the total number of tokens remaining (y) and the number of rolls (x) is a) y = 40x - 8, accounting for the use of 8 tokens from one roll.

Step-by-step explanation:

The student is asking about the function that shows the relationship between y, the total number of tokens remaining, and x, the number of rolls of tokens at an arcade, where each roll contains 40 tokens and a player uses 8 tokens from 1 roll. The correct answer to this question is a) y = 40x - 8. This equation represents that for each roll (x), there are 40 tokens, and if 8 tokens are used from one roll, the remaining tokens in that roll would be 40 - 8, which is 32. However, since we are interested in the total number of tokens remaining across multiple rolls, the function showing the relationship would subtract 8 tokens just once from the total, which would be 40 times the number of rolls (x).

The relationship between the total number of tokens remaining (y) and the number of rolls (x) can be represented by the function y = 40x - 8.

This is because each roll contains 40 tokens, and each time a player uses 8 tokens from a roll, the total number of tokens remaining decreases by 8. Therefore, the function includes the term (-8) to account for the tokens used.

For example, if there are 3 rolls of tokens, the total number of tokens remaining would be y = 40(3) - 8 = 112 tokens.