Question

Sonja has a bank account balance of $1400. Each week, her balance changes by −$85.25. She wants to keep the balance above $377.

For how many weeks will Sonja's balance remain above $377?

Select from the drop-down menu to correctly complete the statement.

Sonja's balance will remain above $377 for
Choose...
weeks.
1. at least 18.
2. fewer than 18.
3. more than 18.

Answer 1

To find out for how many weeks Sonja's balance will remain above $377, we need to determine how many times her balance changes by -$85.25 can be subtracted from $1400 until we reach a balance of $377 or below.

Let's subtract $85.25 repeatedly from $1400 until we reach a balance of $377 or below.

$1400 - $85.25 = $1314.75
$1314.75 - $85.25 = $1229.50
$1229.50 - $85.25 = $1144.25
$1144.25 - $85.25 = $1059.00
$1059.00 - $85.25 = $973.75
$973.75 - $85.25 = $888.50
$888.50 - $85.25 = $803.25
$803.25 - $85.25 = $718.00
$718.00 - $85.25 = $632.75
$632.75 - $85.25 = $547.50
$547.50 - $85.25 = $462.25
$462.25 - $85.25 = $377.00
$377.00 - $85.25 = $291.75

We can see that after 12 weeks, the balance reaches $291.75, which is below $377. Therefore, Sonja's balance will remain above $377 for fewer than 12 weeks.

So, the correct statement is:
Sonja's balance will remain above $377 for fewer than 18 weeks.