{person(1) is A years older than person(2)|person(2) is A years younger than person(1)}. {For the last {four|3|two} years, person(1) and person(2) have been going to the same school.|person(1) and person(2) first met 3 years ago.|} Cardinal(B) years ago, person(1) was C times {as old as|older than} person(2).
How old is person(1) now?
Let person(1)'s current age be personVar(1)
.
That means that B years ago, person(1) was personVar(1) - B
years old.
person(2) is personVar(1) - A
years old right now, so B years ago, he(2) was (personVar(1) - A) - B = personVar(1) - A + B
years old.
person(1) was C times as old as person(2), so that means personVar(1) - B = C (personVar(1) - A + B)
.
Expand: personVar(1) - B = C personVar(1) - C * (A + B)
.
Solve for personVar(1)
to get C - 1 personVar(1) = C * (A + B) - B
; personVar(1) = (C * (B + A) - B) / (C - 1)
.
person(1) is A years older than person(2). Cardinal(B) years ago, person(1) was C times as old as person(2).
How old is person(2) now?
Let person(2)'s current age be personVar(2)
.
That means that person(1) is currently personVar(2) + A
years old and B years ago, person(1) was (personVar(2) + A) - B = personVar(2) + A - B
years old.
Cardinal(B) years ago, person(2) was personVar(2) - B
years old.
person(1) was C times as old as person(2), so that means personVar(2) + A - B = C (personVar(2) - B)
.
Expand: personVar(2) + A - B = C personVar(2) - C * B
.
Solve for personVar(2)
to get C - 1 personVar(2) = A - B + C * B
; personVar(2) = (A - B + C * B) / (C - 1)
.
person(1) is C times as old as person(2) and is also A years older than person(2).
How old is person(1)?
Let person(1)'s age be personVar(1)
.
We know person(2) is 1/C
as old as person(1), so person(2)'s age can be written as personVar(1) / C
.
His(2) age can also be written as personVar(1) - A
.
Set the two expressions for person(2)'s age equal to each other: personVar(1) / C = personVar(1) - A
.
Multiply both sides by C
to get personVar(1) = C personVar(1) - A * C
.
Solve for personVar(1)
to get C - 1 personVar(1) = A * C
; personVar(1) = A * C / (C - 1)
.
person(1) is C times as old as person(2) and is also A years older than person(2).
How old is person(2)?
Let person(2)'s age be personVar(2)
.
We know person(1) is C times as old as person(2), so person(1)'s age can be written as C personVar(2)
.
His(1) age can also be written as personVar(2) + A
.
Set the two expressions for person(1)'s age equal to each other: C personVar(2) = personVar(2) + A
.
Solve for personVar(2)
to get C - 1 personVar(2) = A
; personVar(2) = A / (C - 1)
.
person(1) is A times as old as person(2). Cardinal(B) years ago, person(1) was C times as old as person(2).
How old is person(1) now?
Let person(1)'s age be personVar(1)
.
We know person(2) is 1/A
as old as person(1), so person(2)'s age can be written as personVar(1) / A
.
B years ago, person(1) was personVar(1) - B
years old and person(2) was personVar(1) / A - B
years old.
At that time, person(1) was C times as old as person(2), so we can write personVar(1) - B = C (personVar(1) / A - B)
.
Expand: personVar(1) - B = fractionReduce(C, A) personVar(1) - C * B
.
Solve for personVar(1)
to get fractionReduce(C - A, A) personVar(1) = B * (C - 1)
; personVar(1) = fractionReduce(A, C - A) \cdot B * (C - 1) = A * B * (C - 1) / (C - A)
.
person(1) is A times as old as person(2). Cardinal(B) years ago, person(1) was C times as old as person(2).
How old is person(2) now?
Let person(2)'s age be personVar(2)
.
We know person(1) is A times as old as person(2), so person(1)'s age can be written as A personVar(2)
.
Cardinal(B) years ago, person(1) was A personVar(2) - B
years old and person(2) was personVar(2) - B
years old.
At that time, person(1) was C times as old as person(2), so we can write A personVar(2) - B = C (personVar(2) - B)
.
Expand: A personVar(2) - B = C personVar(2) - B * C
.
Solve for personVar(2)
to get C - A personVar(2) = B * (C - 1)
; personVar(2) = B * (C - 1) / (C - A)
.
In B years, person(1) will be A times as old as he(1) is right now.
How old is he(1) right now?
Let person(1)'s age be personVar(1)
.
In B years, he(1) will be personVar(1) + B
years old.
At that time, he(1) will also be A personVar(1)
years old.
We write personVar(1) + B = A personVar(1)
.
Solve for personVar(1)
to get A - 1 personVar(1) = B
; personVar(1) = B / (A - 1)
.
person(1) is A years old and person(2) is B years old.
How many years will it take until person(1) is only C times as old as person(2)?
Let y
be the number of years that it will take.
In y
years, person(1) will be A + y
years old and person(2) will be B + y
years old.
At that time, person(1) will be C times as old as person(2).
We write A + y = C (B + y)
.
Expand to get A + y = C * B + C y
.
Solve for y
to get C - 1 y = A - C * B
; y = (A - C * B) / (C - 1)
.