Question

at the beginning of the year, juan had $600 in savings and saved an additional $25 each week thereafter. mila started the year with $450 and saved $35 every week. let j represent the amount of money juan has saved t weeks after the beginning of the year and let m represent the amount of money mila has saved t weeks after the beginning of the year. write each function and determine the number of weeks after the beginning of the year until juan and mila have the same amount of money saved.
chart: click twice to plot each line. click a line to delete it. y-axis: total in savings (dollars), x-axis: number of weeks

Explanation:

Step1: Define functions for Juan and Mila

Juan's savings: Initial amount is $60, saves $25 per week. So function is \( J = 60 + 25t \).
Mila's savings: Initial amount is $30, saves $30 per week. So function is \( M = 30 + 30t \).

Step2: Set functions equal to find t

Set \( 60 + 25t = 30 + 30t \).
Subtract \( 25t \) from both sides: \( 60 = 30 + 5t \).
Subtract 30 from both sides: \( 30 = 5t \).
Divide by 5: \( t = 6 \).

Answer:

6 weeks