2-3 days a week swim for 30 min.
3 days a week be in a weight room
either lifting weights, jump roping, or cardio machine
(being active)
for 45 min.
and eating healthy. not cut back on food but eat healthy
how long will it take to lose 10 pounds?
i am 5Ƌ" and 125 pounds

Firstly you dont want to lose "weight" you want to burn body fat
if your weight comes down in a healthy fashion it will take between 5 and 10 weeks. It could be a little quicker but try to ensure it doesnt fly off thats unhealthy.
When you do your exercise make sure you do intervals, this means mixing high and low intensity exercise. This could be 1min sprinting/ 1 min walking trust me when I say its the best way to proceed.
Bottom line, alot of it is trial and error see what you've lost over 2 weeks if its not worked try something else.
P.S
Dont give up on the healthy lifestyle when you've lost that 10 pounds reassign your goal and aim for something else.