Question

Nancy started the year with $425 in the bank and is saving $25 each week. Sam started the year with $705 but is spending $15 a week. When will Nancy and Sam have the same amount of money? How much money will they each have? Write a system of equations that model the following situation. Define each variables with a “Let” statement, write two equations, and solve completely.

Answer 1

The system of equations:

Nancy: Y=$425+$25x

Sam : Y=$705-$15x

Given:

Amount in Nancy's bank = $425

Amount saved by Nancy each week = $25

Amount in Sam's bank = $705

Amount spent by Sam each week = $15

To find:

Y=$425+$25xx

Y=$425+$25x

The system of equations describing the given models.

Solution

1) Amount in Nancy's bank = $425

Amount saved by Nancy each week = $25

Let the number of weeks Nancy saving her money be 'x'.

Let the total amount of money in Nancy's bank after x weeks be 'y'.

The equation for Nancy: Y=$425+$25x

Answer for Nancy

Y=$425+$25x

2) Amount in Sam's bank = $705

Amount spend by Sam each week = $15

Let the number of weeks Sam spending his money be 'x'

Let the total amount of money left in Sam's bank after x weeks ='y'

The equation for Sam:

Y=$705-$15 x x

Answer for Sam: Y=$705-$15x

Explanation: