Hector is 12 years old now. In 4 years he will be twice as old as his sister is then. How old will his sister be next year?
H is Hector's age = 12
S is sister's age.
in 4 yrs H will be 16
in 4 yrs S will be S+4
2(S+4) = 16
S =?
Next yrs S will be ?+1
Is it 4 or 8?
Neither.
2(S+4) = 16
2S + 8 = 16
2S = 8
S = 4 is how old the sister is now.
Next year, what the problem asked, sister will be 5.
To solve this problem, let's break it down step by step:
1. Let's assume Hector's sister's current age is x.
2. According to the problem, in 4 years, Hector will be twice as old as his sister is then. So, in 4 years, Hector will be 12 + 4 = 16 years old.
3. Hector will be twice as old as his sister, so: 16 = 2 * (x + 4).
4. Simplifying the equation, we have: 16 = 2x + 8.
5. Subtracting 8 from both sides, we get: 8 = 2x.
6. Dividing both sides by 2, we have: x = 4.
7. Therefore, Hector's sister's current age is 4 years old.
Now that we know Hector's sister is currently 4 years old, we can determine how old she will be next year:
Since Hector is currently 12 years old, next year he will be 12 + 1 = 13 years old.
Similarly, Hector's sister will be 4 + 1 = 5 years old next year.
Therefore, Hector's sister will be 5 years old next year.