SOLUTION: Faith is 10 years older than Grace. Eight years ago, Faith was 3 times Grace's age. How old are they now?

Question 1164417: Faith is 10 years older than Grace. Eight years ago, Faith was 3 times Grace's age. How old are they now?
Found 3 solutions by AndrewWillie, ikleyn, greenestamps:
Answer by AndrewWillie(2)   (Show Source): You can put this solution on YOUR website!
I think Fainth 32 and Grace 22
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.
Faith is 10 years older than Grace. Eight years ago, Faith was 3 times Grace's age. How old are they now?
~~~~~~~~~~~~~~~~

Let x be the Grace age; Then Faith is (x+10) years old. Eight years ago they were (x-8) (Grace) and ((x+10)-8) = (x+2) (Faight) years old. The condition says x+2 = 3*(x-8). From this equation x+2 = 3x - 24 2 + 24 = 3x - x 26 = 2x x = 26/2 = 13. ANSWER. Grace is 13 years old; Faith is 13+10 = 23 years old. CHECK. 8 years age they were 13-8 = 5 and 23-8 = 15 years old with the ratio = 3. ! Correct !

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.

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

The difference in their ages is 10 years; 8 years ago, Faith's age was 3 times Grace's age.

Let x be Grace's age 8 years ago; then Faith's age 8 years ago was 3x. The difference in their ages then was 3x-x = 2x.

But the difference in their ages then was 10 years. So 2x=10, and x=5.

That means their ages 8 years ago were x=5 and 3x=15.

And that means their current ages are 13 and 23.

RELATED QUESTIONS
John is 7 years older than his sister Mary Grace. In 10 years John will... (answered by josgarithmetic)
in 4 years John will be four thirds Graces age 5 years ago John was one year more than... (answered by hamsanash1981@gmail.com)
Eight years ago, Ed was ten times as old as his youngest daughter Faith. In six years, he (answered by richwmiller,AndrewWillie,josgarithmetic,ikleyn,greenestamps)
Jordan is now four times older than Grace. In 30 years, he will be 18 years older than... (answered by heracross98)
peter is twice as old as Paul who in turn is 5 years older than Grace. if their total age (answered by Alan3354)
Mommy Grace is 27yrs old. Her son is 13yrs old. How many years ago was Mommy Grace 3... (answered by josgarithmetic,larrypizzu )
please help me with these problems: 1. Olan is 3 years older than his sister, Rose.... (answered by ankor@dixie-net.com)
Eight years ago, the sum of Pete's age and Matt's age was 26. Matt is 4 years older than... (answered by josgarithmetic)
Miriam is 10 years older than Ricardo. Two years ago, Miriam was 3 times as old as... (answered by jorel1380)