Question

A teacher has two students, one two times as old as the other. The teacher is five times as old as the older student, and in 5 years she will be five times as old as her younger student. Find the teacher’s present age.

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Answer 1

By setting up equations based on the relationships between the students' and teacher's ages, we determine the teacher's present age to be 40 years old.

Step-by-step explanation:

To solve for the teacher's present age, we need to set up equations based on the information given:

1. Let's denote the younger student's age as x.
2. The older student is two times as old as the younger student, so their age is 2x.
3. The teacher is five times as old as the older student, so the teacher's age is 5(2x) = 10x.
4. In 5 years, the teacher will be five times as old as the younger student's age at that time, which leads to the equation 10x + 5 = 5(x + 5).

Solving the last equation:

10x + 5 = 5x + 25

Subtract 5x from both sides:

5x + 5 = 25

Now, subtract 5 from both sides:

5x = 20

Divide both sides by 5:

x = 4

We found that the younger student is 4 years old. Using this value, we can find the teacher's present age:

The older student's age is 2(4) = 8 years old.

The teacher's present age is 5(8) = 40 years old.

Answer 2

There is no way to find the teachers present age as neither the students bore the teachers age was given.