Let's solve this problem step by step.
Problem:
A father is 30 years older than his son.
Five years ago, the father was four times as old as his son.
We need to find the son's current age.
Step 1: Define Variables
Let's define the son's current age as SS years. Then the father's current age would be S+30S+30 years.
Step 2: Set Up the Equation for 5 Years Ago
Five years ago, the son's age was S−5S−5 years, and the father's age was (S+30)−5=S+25(S+30)−5=S+25 years.
According to the problem, five years ago, the father was four times as old as his son:
S+25=4×(S−5)
Step 3: Solve the Equation
Now, let's solve the equation:
S+25=4(S−5)
First, distribute the 4 on the right side:
S+25=4S−20
Next, get all the terms involving SS on one side by subtracting SS from both sides:
25=3S−20
Now, add 20 to both sides:
45=3S
Finally, divide by 3 to find SS:
S=15