Question

Using a Linear Function to Solve a Problem
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. How much money was Alma given as a gift?

$

Answer 1

Let G be the initial gift and w the monthly withdrawal. After n months the balance is G − n·w.

Given:
G − 5w = 442
G − 13w = 226

Subtract the second from the first:
( G − 5w ) − ( G − 13w ) = 442 − 226
8w = 216 → w = 27

Then G = 442 + 5·27 = 442 + 135 = 577.

Alma was given $577.