The sum of the ages of mingfa and his father is 34 years.in 4 years time,the square of mingfas age will be equal to his fathers age. Find mingfas present age.
mingfas present age is 2.
Enjoy!
Thanks,but can you explain how
yes mingfas is 2 and his father is 32 , after 4 years mingfas will be 6 and his father will be 36.
so the square of mingfas age will be 36 which will be exactly the age of his father
To find Mingfa's present age, we need to solve this problem step by step.
1. Let's assume that Mingfa's age is "M" and his father's age is "F".
2. We are given that the sum of their ages is 34 years, so we can write the equation: M + F = 34.
3. In 4 years, Mingfa's age will be M + 4, and his father's age will be F + 4.
4. According to the given condition, the square of Mingfa's age in 4 years will be equal to his father's age: (M + 4)^2 = F + 4.
5. We can rewrite the equation as: M^2 + 8M + 16 = F + 4.
6. Now we have two equations:
- M + F = 34
- M^2 + 8M + 16 = F + 4.
7. We can solve the first equation for F by subtracting M from both sides: F = 34 - M.
8. Substituting this value into the second equation, we get: M^2 + 8M + 16 = 34 - M + 4.
9. Simplifying the equation, we have: M^2 + 9M - 14 = 0.
10. Now we can solve this quadratic equation using factoring or the quadratic formula. In this case, the equation factors as: (M - 2)(M + 7) = 0.
11. From this, we get two possible solutions: M = 2 and M = -7.
12. Since Mingfa's age cannot be negative, we discard the solution M = -7.
13. Therefore, Mingfa's present age is 2 years old.