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In the given problem, apply your knowledge in algebra and basic mathematics specially in solving linear equation.

The problem is an application of linear equation having three unknown variables.

Let

x is age of Roy

y is age of Boyet

z is age of Bong

Solution

Create three equation to solve three unknown variables.

First Equation

The sum of The sumof the ages of Roy, Boyet and Bong is 12.

x + y + z = 12

Second Equation

Boyet is 3 years younger than Roy.

y = x - 3

Third Equation

Roy is 6 years older than Bong.

x = z + 6

Solution

x + y + z = 12

y = x - 3

x = z + 6

y = x - 3 → y = (z + 6) - 3

x + y + z = 12 → (z+6) + [(z+6)-3] + z = 12

Simplify

(z+6) + [(z+6)-3] + z = 12

z + 6 + z + 3 + z = 12

3z + 9 = 12

Solve for z

3z + 9 = 12

3z = 12-9

3z = 3

z = 1

z = 1

x = z+6

x = 1+6

x = 7

y = x-3

y = 7-3

y = 4

Check:

x+y+z= 12

7+4+1 = 12 ✓

Answer:

4 years old

Learn more about solving linear equation here at brainly.ph/question/10870214

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