At the arcade, nick spent 203 tokens on videogames 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?

Suppose nick spent x number of tokens on day 1

So he spent x + 5 on day 2

He spent x + 10 on day 3

He spent x + 15 on day 4

He spent x + 20 on day 5

On day 6 he spent x + 25

And on day 7 he spent x + 30

So in all he spent

x + x + 5 + x + 10 + x + 15 + x + 20 + x + 25 + x + 30

= 7x + 105

But total token spent = 203

So

7x + 105 = 203

Subtracting 105 from both sides

7x = 203 - 105

7x = 98

Dividing by 7 on both sides

x = 14

So on third day he spent x + 10

= 14 + 10

= 24 tokens

Tokens spent on day 3 = 24

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.