Perry currently has $350 dollars and is If 7 times a number is decreased by 33,
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?
Let's solve this problem step by step.
Let's assume that after "x" days, Perry and Nick will have the same amount of money.
After "x" days, Perry will have $350 - ($6 * x) dollars.
After "x" days, Nick will have $8 * x dollars.
We can set up an equation to find the value of "x":
$350 - ($6 * x) = $8 * x
Let's solve for x:
$350 - 6x = 8x
350 = 8x + 6x
350 = 14x
x = 350 / 14
x ≈ 25
After approximately 25 days, Perry and Nick will have the same amount of money.
Let's set up equations to represent the situation for Perry and Nick:
Perry's money after "x" days can be represented as:
Perry's initial money - (amount spent per day * number of days)
P = 350 - (6 * x)
Nick's money after "x" days can be represented as:
Nick's initial money + (amount earned per day * number of days)
N = 0 + (8 * x)
To find when they will have the same amount of money, we need to solve the equation P = N.
350 - (6 * x) = 0 + (8 * x)
Now, we can solve for "x":
350 - 6x = 8x
Combine like terms:
350 = 14x
Divide both sides by 14:
350/14 = 14x/14
25 = x
Therefore, they will have the same amount of money after 25 days.
To find out after how many days Perry and Nick will have the same amount of money, we need to set up an equation and solve for the number of days.
Let's assume the number of days is represented by "d".
Perry's money after d days can be calculated using the equation:
Perry's money = Initial money - (Spending per day * Number of days)
Perry's money = $350 - ($6 * d)
Nick's money after d days can be calculated using the equation:
Nick's money = (Earnings per day * Number of days)
Nick's money = $0 + ($8 * d)
We want to find the number of days when Perry and Nick have the same amount of money. So, we can set up the equation:
$350 - ($6 * d) = $0 + ($8 * d)
Now, let's solve for d:
$350 - $6d = $8d
Combine like terms:
$350 = $14d
Divide both sides by $14:
d = $350 / $14
d = 25
Therefore, after 25 days, Perry and Nick will have the same amount of money.