Question

A Wizard named Nepo says, "I am only three times my son's age. My father is to years more than twice my age. Together the three of us are a mere 1240 years old." How old is Nepo?

a) 310 years old
b) 400 years old
c) 490 years old
d) 580 years old

Answer 1

Using algebra, we find that the wizard Nepo is 360 years old by setting up equations for the ages and solving them. This does not match any of the provided options, which suggests a possible typo in the question.

Step-by-step explanation:

To solve for the age of the wizard Nepo, we can set up a system of equations based on the information given:
Let N represent Nepo's age, S represent his son's age, and F represent his father's age.

• Nepo is three times his son's age: N = 3S.
• Nepo's father is 40 years more than twice Nepo's age: F = 2N + 40.
• Together, their ages sum to 1240 years: N + S + F = 1240.

Substituting the first two equations into the third gives us:
N + (N/3) + (2N + 40) = 1240
Multiplying all terms by 3 to remove the fraction and simplifying:

3N + N + 6N + 120 = 3720

Combining like terms:

10N + 120 = 3720

Subtracting 120 from both sides:

10N = 3600

Dividing both sides by 10:

N = 360

Therefore, Nepo is 360 years old, which is not listed in the provided options. So it could be assumed that there was a typo in the question or provided options.