At the arcade, Nick spent 203 tokens on video games in seven days. Each day he spent five more tokens than the previous day. How many tokens did Nick spend on the third day at the arcade?

At the arcade, Nick spent 203 tokens on video games in seven days. Each day he spent five more tokens than the previous day. How many tokens did Nick spend on the third day at the arcade?

Detailed Explanation

To determine how many tokens Nick spent on the third day at the arcade, we need to calculate the total number of tokens he spent on the previous two days and then add five tokens to that amount.

Let's break down the problem day by day:

On the first day, Nick spent x tokens.

On the second day, he spent x + 5 tokens.

On the third day, he spent x + 5 + 5 = x + 10 tokens.

We know that Nick spent a total of 203 tokens over the seven days, so we can set up the following equation:

x + (x + 5) + (x + 10) + (x + 15) + (x + 20) + (x + 25) + (x + 30) = 203

Simplifying the equation:

7x + 105 = 203 = 203 - 105 = 98

x = 98 ÷ 7 = 14

Therefore, Nick spent 14 tokens on the first day. To find the number of tokens he spent on the third day, we substitute x = 14 into the equation:

x + 10 = 14 + 10 = 24

So, Nick spent 24 tokens on the third day at the arcade.