Problem
The age of Peter is a third of his father’s age, but in 10 years his father will only be two times as old as Peter will be. What is Peter’s age today?
Modeling Steps
HINT: Let x be the age of Peter (I) today, and y be the age of his father today. Can you write down the conditions now? SOLUTION: The age of the father is y, and also 3x (he is three times as old as his son), hence: y = 3x. In ten year, the father is y + 10 year old, but also 2(x + 10), hence: y + 10 = 2(x + 10). Therefore the mathematical model is:
Now it’s easy to solve the model: x = 10 and y = 30.
model AgeOfPeter "How old is Peter";
variable x; y;
constraint A: y = 3*x;
B: y+10 = 2*(x+10);
solve;
Write('The age of Peter is: %d' n', x);
end
References
[1] MatMod. Homepage for Learning Mathematical Modeling : https://matmod.ch.
[2] Hürlimann T. Reference Manual for the LPL Modeling Language, most recent version. https://matmod.ch/lpl/doc/manual.pdf.