SOLUTION: 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 st

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Question 1133073: 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.
PLS HELP!
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
Let x= Age of younger student
Then
2x is the age of the older student
5(2x)=10x is the age of the teacher

10x+5 = 5(x+5)
Solve the above for x to get x=4 —> teacher is 10x=40 years old
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Ans: the teacher is 40 years old
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Check:
Younger student is 4
Older student is 2*4=8
Teacher is 40 (=5*8, in agreement with teacher being 5 times as old as older student)
In 5 years,
Younger student will be 9
Teacher will be 45 (= 9*5, so this answer checks)
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
From the condition, the students ages are x and 2x, while the teacher age is 5*(2x) = 10x years.


The condition also says that


    10x + 5 = 5*(x+5)    ("in 5 years she (= the teacher) will be five times as old as her younger student".)


Solve this equation and complete the solution on your own.


ANSWER.  The teacher is 40 years old.

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There is a bunch of lessons on age word problems
    - Age problems and their solutions
    - A fresh formulation of a traditional age problem
    - Really intricate age word problem
    - Selected age word problems from the archive
    - Age problems for mental solution
in this site.

Read them and become an expert in solving age problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Age word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

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