A half of what John's age was 4 years ago is equal to one third of what it will be in 5 years' time. How old is John now? Explain your workings
Let John's present age be x
Four years ago John was x-4
Half of John's age 4 years ago = (x-4)/2
John's age in 5 years from now = x+5
a third of his age 5 from now = (x+5)/3
(x-4)/2 = (x+5)/3
cross-multiply
3x - 12 = 2x + 10
x = 22
So John is now 22 years old
check:
4 years ago he would have been 18
5 years from now he will be 27
is half of 18 equal to a third of 27 ? YES
To solve this problem, let's start by assigning variables. Let's say John's current age is 'x'.
From the given information, we can break down the problem into two parts:
Part 1: A half of what John's age was 4 years ago is equal to...
Since John's age 4 years ago would have been (x - 4), we can rewrite this part of the problem as:
(1/2) * (x - 4)
Part 2: ...one third of what it will be in 5 years' time.
In 5 years' time, John's age will be (x + 5). So, one-third of what it will be in 5 years' time can be written as:
(1/3) * (x + 5)
Now, we can set up an equation with the two parts and solve for John's age, x.
(1/2) * (x - 4) = (1/3) * (x + 5)
To simplify this equation, we can multiply both sides by 6 to get rid of the fractions:
6 * [(1/2) * (x - 4)] = 6 * [(1/3) * (x + 5)]
3 * (x - 4) = 2 * (x + 5)
Distribute the multiplication:
3x - 12 = 2x + 10
Bring the variables to one side and the constants to the other side:
3x - 2x = 10 + 12
x = 22
Therefore, John is currently 22 years old.