Judy has $20 and is saving at a rate of $6 per week. ida has $172 and spending at a rate of $4 per week. after how many weeks will each have the same amount?

Let
x> number of weeks
y> total money

we know that
Judy's saving equation can be modeled as follows
y=20+6x> equation 1

and 
Ida's spending equation can be modeled as follows
y=172-4x> equation 2

to know when they will have the same amount
equation 1=equation 2
20+6x=172-4x> 6x+4x=172-20> 10x=152> x=15.2
x=15.2 weeks

the answer is 15.2 weeks