Uncle Bill is 6 times as old as John and he will be 4 times as old as John in 4 years' time. If Uncle Bill is less than 60 years of age, how old will he be in 6 years' time?
Please show working out as well, thanks.
John's present age --- x
Uncle's present age ---- 6x
in 4 year's time:
John will be x+4
Uncle's age will be 6x + 4
6x+4 = 4(x+4)
6x+4 = 4x + 16
2x = 12
x = 6
John is now 6 and the uncle is now 36
in 6 years time the uncle will be 42
uncle's in 6 years time = 6x+6
To solve this problem, let's first assign some variables:
Let's say John's age is represented by "J" and Uncle Bill's age is represented by "B".
According to the problem:
1. Uncle Bill is 6 times as old as John: B = 6J.
2. In 4 years' time, Uncle Bill will be 4 times as old as John: B + 4 = 4(J + 4).
Now, we can solve the system of equations:
Substitute B in the second equation with 6J from the first equation:
6J + 4 = 4(J + 4).
Simplify the equation:
6J + 4 = 4J + 16.
Move all the terms with J to one side and the constant terms to the other side:
6J - 4J = 16 - 4.
Combine like terms:
2J = 12.
Divide both sides of the equation by 2 to solve for J:
J = 6.
Now we know John's age, we can substitute this value back into the first equation to find Uncle Bill's age:
B = 6J = 6(6) = 36.
Since Uncle Bill is less than 60 years of age, we know that he will not reach the age of 60 in 6 years' time. Therefore, his age in 6 years' time will still be 36 years old.