John is eight year older than his sister.In three years,he will be as twice as she will be then.
How old are they both now?
J = John present age
S = sister present age
J = S + 8
After 3 years John wil be J + 3 yrs old.
Sister wil be S + 3 yrs old.
In three years,he will be as twice as she will be then mean:
( J + 3 ) / ( S + 3 ) = 2
In this equation replace J with S + 8
( S + 8 + 3 ) / ( S + 3 ) = 2
( S + 11 ) / ( S + 3 ) = 2
Multiply both sides by S + 3
S + 11 = 2 ( S + 3 )
S + 11 = 2 S + 6
Subtract 6 to both sides
S + 11 - 6 = 2 S + 6 - 6
S + 5 = 2 S
Subtract S to both sides
S + 5 - S = 2 S - S
5 = S
S = 5
J = S + 8 = 5 + 8 = 13
John is 13 yrs old, sister is 5 yrs old.
Proof:
After 3 years John wil be 13 + 3 = 16 yrs old
Sister wil be 5 + 3 = 8 yrs old
16 / 8 = 2
Sister: X yrs. old.
John: x + 8 yrs. old.
3 yrs. later:
Sister: x + 3.
John: (x+8) + 3 = x + 11.
x + 11 = 2(x + 3),
X = 5.
x + 8 = 5 + 8 = 13.
To solve this question, let's use algebra to represent the information given.
Let's assume John's current age is 'J' and his sister's current age is 'S'.
Based on the given information, we can form two equations:
1. "John is eight years older than his sister": J = S + 8
2. "In three years, he will be as twice as she will be then": J + 3 = 2 * (S + 3)
Now, let's solve the equations to find the values of J and S.
Substitute the value of J from the first equation into the second equation:
S + 8 + 3 = 2 * (S + 3)
S + 11 = 2S + 6
S - 2S = 6 - 11
-S = -5
Since -S is equal to -5, we can multiply both sides by -1 to isolate S:
S = 5
Using the value of S in the first equation to find J:
J = S + 8
J = 5 + 8
J = 13
Therefore, John is currently 13 years old, and his sister is currently 5 years old.