Penny currently has $180 dollars and is spending $6 per day. Nick has no money but is earning $8 each day. After how many days will they have the same amount of money

They'll have the same amount of money after 90 days.

Step-by-step explanation:

The amount of money Penny has after "x" days is the sum of the initial amount she had (180) plus the product of the days that passed with how much she gets each day. This can be expressed in the following equation:

Penny = 6*x + 180

The amount of money Nick will have can be expressed in the same way, but he didn't have any money in the beggining so it'll be only the amount he gets each day. We have:

Nick = 8*x

To know the amount of days it'll take for them to have the same amount we need to make the two equations equal. We have:

Penny = Nick

6*x + 180 = 8*x

8*x - 6*x = 180

2*x = 180

x = 180/2 = 90 days

They'll have the same amount of money after 90 days.