"How Old Is Ann?"?

Question

One of the most famous puzzles in the math world is "How Old Is Ann?" Here's another variation. Ann is now exactly two-fifths of her older sister's age, and two years from now she will be one-half of her older sister's age. Conversely, two years ago, Ann was only one-fourth the age of her older sister's age at that time. How old is Ann now? (She's a fairly young child, by the way)

Answer 1

[#1] A = .40 (S) [Ann is 4/10 x Sister's age]
[#2] A + 2 = .50 (S + 2) [in 2 years, Ann is 5/10 Sister's age]
[#3] A - 2 = .25 (S - 2) [2 yrs before, Ann = 1/4 Sister's age]

[#4] 2A = .75 S + .50 [combine last two lines # 2 and #3]

.80 S = .75 S + .50 [plug "A = .40 S" from #1 into #4]

.05 S = .50 [subtract ".75 S" from both sides]

5 S = 50 [multiply both sides by 100 to get rid of decimals]

S = 10 [divide both sides by 5 to find S = Sister's age]
A = 4 [plug S = 10 into other equations to get A = Ann's age]

Check your answers by plugging into all three equations.
Ann = 4 years old (fairly young)
Sister = 10 years old

The trick to the other two equations is to add +2 to "both"
S and A to get their ages two years later (S+2 and A+2), or to subtract -2 from "both" to get their ages two years ago
(S-2 and A-2).