Difficult math problems! Please help?

Question

3. Three years ago, Annie was three times as old as her sister. Now Annie is twice as old as her sister. How old is Annie now?

5. The exterior dimensions of an empty cooler in the shape of a rectangular prism are 18 inches by 18 inches by 24 inches. For insulation, the top, the bottom, and each of the four walls are two inches thick. What is the volume of the empty space inside the cooler?

6. A month ago, the ratio of nurses to doctors on a hospital staff was 3:5. Since that time, two additional nurses joined the staff, no nurses left, and the number of doctors remained the same. The ratio of nurses to doctors on the hospital staff is now 4:5. How many nurses are now on the staff?

Any and all help would be greatly appreciated. Thanks so much! Please explain how you got your answers :)

Answer 1

annie now = A
sister now = s
a-3 = 3(s-3)
a = 2s
2s - 3 = 3s - 9
6 = s
A = 12
check:
three years ago Annie was 9 and sister was 3.
checks

5. (18 - 4)(18-4)(24-4) = 14*14*20 = 3920 cubic inches
I subtracted 2*2" from each of the exterior dimensions to get the interior dimensions.

6.
5n = 3d (original ratio)
5(n+2) = 4d (new ratio0
5n + 10 = 4d
10 = d (there are ten doctors)
there were 6 nurses; now there are eight.