10 weeks
Let x represent weeks
Barb: 800-30x
Claire: 300+20x
Set the 2 equations equal to each other
800-30x=300+20x
Add the 30x over
800=300+50x
Subtract the 300 over
500=50x
Divide by 50 on both sides
x=10
After 10 weeks they will have the same amount of money.
Hope this helps!