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Question 5

i) A father is 30 years older than his son. After 5 years, the age of the father will be four times his son's age. The present age of the son is [tex]\(X\)[/tex] years. Establish an equation and determine the age of the son. (3)

Sagot :

GinnyAnsweridn
Sure, let's work through the problem step by step.

### Given Information:
1. A father is 30 years older than his son.
2. After 5 years, the father's age will be four times his son's age.

### Let:
- [tex]\( X \)[/tex] be the present age of the son in years.

### Step 1: Express the Father's Current Age in Terms of [tex]\( X \)[/tex]
Since the father is 30 years older than his son:
- Father's present age = [tex]\( X + 30 \)[/tex].

### Step 2: Determine Ages After 5 Years
In 5 years, both the father and son will be 5 years older:
- Son's age after 5 years = [tex]\( X + 5 \)[/tex].
- Father's age after 5 years = [tex]\( (X + 30) + 5 = X + 35 \)[/tex].

### Step 3: Establish an Equation Based on the Given Condition
It is given that after 5 years, the father's age will be four times the son's age:
[tex]\[ X + 35 = 4(X + 5) \][/tex]

### Step 4: Simplify the Equation
Let's solve for [tex]\( X \)[/tex] step by step:
[tex]\[ X + 35 = 4(X + 5) \][/tex]
[tex]\[ X + 35 = 4X + 20 \][/tex]

Next, we isolate [tex]\( X \)[/tex] on one side:
[tex]\[ 35 - 20 = 4X - X \][/tex]
[tex]\[ 15 = 3X \][/tex]

Solve for [tex]\( X \)[/tex]:
[tex]\[ X = \frac{15}{3} \][/tex]
[tex]\[ X = 5 \][/tex]

### Step 5: Conclusion
The present age of the son is [tex]\( 5 \)[/tex] years.
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