Question

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 $n$?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 $n$?

Answer 1

7

Explanation:

If the youngest sister is n years old, then Lana must be 2n, and the twin sisters are each 2n - 2. So, the total of all four sisters' ages is

n + 2n + (2n - 2) + (2n - 2).

Collecting like terms, we can simplify this sum to 7n - 4 = 45. We know that the sum of the four sisters' ages is 45, so we have the equation

7n - 4 = 45.

Adding 4 to both sides gives 7n = 49, then dividing both sides by 7 gives n.Therefore, the youngest sister is 7 years old.

Answer 2

Let the youngest sister be n years
Lana will be 2n years, as her youngest sister is half her age
The age of the twins separately will be 2n-2 as they are 2 years younger than Lana
So, the equation looks like this:
n + 2n + 2(2n-2) = 45
Now solve for n:
3n + 4n - 4 = 45
7n - 4 = 45
7n = 49
n = 7
So the youngest sister is 7, Lana is 14 and the twins are 12. 14 + 12 + 12 + 7 =45