SOLUTION: Ben is six years younger than his sister. After 10 years the sum of their ages will be 50. What are their present ages?

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Question 1153882: Ben is six years younger than his sister. After 10 years the sum of their ages will be 50. What are their present ages?
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
x-6, Ben
x, Sister



.
.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


A solution without formal algebra -- using logical reasoning and simple arithmetic instead....

If the sum of their ages 10 years from now will be 50, then the sum now is 30.

So the two ages are two whole numbers with a sum of 30 and a difference of 6.

One way to solve this kind of problem quickly is to reason that the two numbers 15 and 15 have a sum of 30 but are the same; to get a sum of 30 with a difference of 6 between the two numbers, add 3 to one of the 15s and subtract 3 from the other -- giving you the numbers 18 and 12.

ANSWER: Ben is 12; his sister is 18.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

            Since the equation is written  INCORRECTLY  in the post by @josgarithmetic,
            I came to bring a correct Algebra solution. 


Let sister's age be x; then Ben's age is (x-6).


In 10 years, their ages are (x+10)  and  ((x-6)+10).


So, the equation for the total age in 10 years is


    (x+10) + ((x-6)+10) = 50.


Simplify and solve


    2x + 14 = 50

    2x      = 50 - 14 = 36.

     x                = 36/2 = 18.


ANSWER.  The sister is 18 years old.  Ben is 18-6 = 12 years old.

Solved.

------------------

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 problems
    - Selected age word problems from the archive
    - Age problems for mental solution
    - Miscellaneous age problems
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

to your archive and use it when it is needed.


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