John is 3 times as old as Susan now. In 4 years time John will be 18 years older than Susan. Find John's age and Susan;s age now.
present ages:
Susan --- x
John ---- 3x
Four years from now:
Susan -- x+4
John --- 3x + 4
3x+4 = x+4 + 18
2x = 18
x = 9
Susan is now 9 and John is now 27
check:
in four years:
Susan = 13, John is 31
is 31 greater than 13 by 18 ? YES!!
To find John's age and Susan's age, we can set up a system of equations based on the given information.
Let's represent John's current age as "J" and Susan's current age as "S".
1. From the first sentence, we know that John is currently 3 times as old as Susan, so we can write the equation:
J = 3S ---- (Equation 1)
2. From the second sentence, we know that in 4 years, John will be 18 years older than Susan, so we can write the equation:
J + 4 = S + 18 ---- (Equation 2)
Now we have a system of two equations with two variables. We can solve these equations simultaneously to find the values of J and S.
1. Substitute the value of J from Equation 1 into Equation 2:
3S + 4 = S + 18
2. Simplify the equation:
3S - S = 18 - 4
2S = 14
3. Divide both sides of the equation by 2:
S = 7
4. Substitute the value of S into Equation 1 to find J:
J = 3S
J = 3(7)
J = 21
Therefore, John is currently 21 years old, and Susan is currently 7 years old.