John’s age is 3/5 of his sister’s age. The total age in four years time is 24 years. How old is John now? Show steps.
Let's start by setting up equations based on the information given:
Let x be John's age now and y be his sister's age now.
We know that John’s age is 3/5 of his sister’s age, so we can write the equation:
x = 3/5 * y
In four years time, John will be x + 4 years old and his sister will be y + 4 years old. We are also given that the total age in four years time is 24 years, so we can write the equation:
(x + 4) + (y + 4) = 24
Now, we can substitute the expression for x from the first equation into the second equation:
(3/5 * y + 4) + (y + 4) = 24
3/5y + 4 + y + 4 = 24
3/5y + y + 8 = 24
8/5y + 8 = 24
8/5y = 16
y = 10
Now that we have found y, we can substitute it back into the first equation to find x:
x = 3/5 * 10
x = 6
Therefore, John is 6 years old now.