Lana is the oldest of four sisters. her youngest sister is half her age. the other two sisters are twins 2 years younger than lana. when the four sisters' ages are added together, the result is 45. if the youngest sister is n years old, what is n? will give meadel

If Lana's age is L, her youngest sister is L/2 (or 0.5L) and the twins L-2.  Add all these together (remember that there are two sisters who are L-2 years old):
0.5L + L-2 + L-2 + L = 45
Simplify the L's by adding them all together, we get:
3.5L - 2 - 2 = 45
3.5L - 4 = 45
Now add 4 to both sides:
3.5L = 49
Now divide both sides by 3.5
L = 49/3.5 = 14.  Now we know that Laura is 14, so her youngest sister must be 7.