Chen’s father was 25 when Chen was born. In 5 years Chen will be exactly half his father’s age.
a. Try to figure out how old Chen is now. Describe how you got your answer.
b. Now solve the problem using equations.
in 5 years father will be 30.
So, Chen will be 15.
So, Chen is now 10.
no, forget that.
father is c+25
in five years,
c+25+5 = 2(c+5)
c = 20
so, Chen is 20, and father is 45. In 5 years, he will be 25 and his father will be 50.
a. To figure out how old Chen is now, we can start by considering the information given. Chen's father was 25 when Chen was born, which means there is a 25-year age difference between them. In 5 years, Chen will be exactly half his father's age, which implies that at that time, the age difference will still remain constant.
So, in 5 years, Chen's age will be half of his father's age. Let's assume that Chen's current age is C. In 5 years, Chen's age will be C + 5, and his father's age will be (C + 5) + 25 (due to the initial 25-year age difference).
According to the given information, we can set up the equation: C + 5 = (C + 5) + 25 / 2
Simplifying this equation, we get: 2(C + 5) = (C + 5) + 25
Expanding and simplifying further, we have: 2C + 10 = C + 30
Subtracting C from both sides, we get: C + 10 = 30
Finally, subtracting 10 from both sides gives us: C = 20
Therefore, Chen is currently 20 years old.
b. Let's solve the problem using equations:
Let C be Chen's current age and F be his father's current age.
According to the given information:
1. Chen's father was 25 when Chen was born, so F - C = 25.
2. In 5 years, Chen will be exactly half his father's age, so C + 5 = (F + 5) / 2.
We can solve this system of equations to find their current ages.
From equation 1, we have: F = C + 25.
Substituting this value of F into equation 2, we get: C + 5 = (C + 25 + 5) / 2.
Simplifying this equation, we have: C + 5 = (C + 30) / 2.
Expanding the right side, we get: C + 5 = C/2 + 15/2.
Multiplying both sides by 2 to eliminate the fraction, we have: 2(C + 5) = C + 15.
Expanding the left side, we get: 2C + 10 = C + 15.
Subtracting C from both sides, we have: 2C - C + 10 = C - C + 15.
Simplifying further, we get: C + 10 = 15.
Subtracting 10 from both sides gives us: C = 15 - 10.
Therefore, Chen is currently 5 years old.