Alma was given some money as a gift and deposited it into a savings account. She makes a withdrawal of the same amount at the end of each month. At the end of the 5th month, her balance was $442. At the end of the 13th month, her balance was $226. What is the input?

$577

Step-by-step explanation:

Let y = amount of money in the account.

Let x = number of months.

The withdrawals are always the same amount and occur every month, so this is a linear relation.

We are given two points of the relation: (5, 442) and (13, 226).

y = mx + b

m = (442 - 226)/(5 - 13) = 216/(-8) = -27

The slope, -27, represents the amount she withdraws each month.

y = -27x + b

442 = -27(5) + b

442 = -135 + b

b = 577

y = -27x + 577

b = y-intercept = initial amount

The input was $577.