A teacher has two students, one three 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.
That is wrong - the answer is 40
To solve this problem, we can use a system of equations.
Let's assume:
The age of the younger student = x
The age of the older student = 3x
The age of the teacher = 5(3x) = 15x
In 5 years, the younger student's age will be x + 5, and the teacher's age will be 15x + 5.
According to the problem, the teacher's age in 5 years will be five times the younger student's age.
15x + 5 = 5(x + 5)
Let's solve the equation:
15x + 5 = 5x + 25
10x = 20
x = 2
Therefore, the age of the younger student is 2.
To find the teacher's age, substitute x = 2 into the equation:
Teacher's age = 15x = 15 * 2 = 30
So, the teacher's present age is 30.
S = 3s ... t = 5S = 15s
t + 5 = 5(s + 5) = 5s + 25
3t + 15 = 15s + 75
substituting ... 3t + 15 = t + 75
solve for t