SOLUTION: Sarah is currently four times as old as her daughter Linda. in 6 years Sarah will be three time as old as Linda. calculate Linda's current age.

Question 1163312: Sarah is currently four times as old as her daughter Linda.
in 6 years Sarah will be three time as old as Linda.
calculate Linda's current age.
Found 3 solutions by Theo, ikleyn, Alan3354:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
s = sarah's age now.
l = linda's age now.
sarah is currently 4 times as old as linda.
that gets you:
s = 4 * l
in 6 years, sarah will be 3 times as old as linda.
that gets you:
s + 6 = 3 * (l + 6)
simplify this equation and subtact 6 from both sides to get:
s = 3 * l + 12
since s = 4 * l from the first equation, replace s with 4 * l to get:
4 * l = 3 * l + 12
solve for l to get:
l = 12
s = 4 * l = 48
in 6 years s is 54 and l is 18.
at that time, s = 3 * l because 3 * 18 = 54.

be careful how your word your problem.
3 times as old is not the same as 3 times older.
if the current age is 10, then 3 times as old makes the new age equal to 30 which is 20 more than 10 which is 2 times older than 10.
if the current age is 10, then 3 times older makes the new age equal to 40 which is 30 more than 10 which is 3 times older than 10, but 4 times as old as 10.

to put it another way:
y = 3x means y is 3 times as large as x.
y = 3x + x means y is 3 times larger than x which means that y = 4 times as much as x.

your problem works with 3 times as much.
it does not work with 3 times larger because 3 times larger means 4 times as large.
solve for 3 times larger, you get:
y = 4x
y + 6 = 3 * (x + 6) + (x + 6) which becomes y + 6 = 4 * (x + 6) which becomes y + 6 = 4 * x + 24 which becomes y = 4 * x + 18
y = 4 * x and y = 4 * x + 18 yield two straight line equations that have the same slope, therefore parallel to each other, therefore will never intersect, so there's no way to solve for x.
on the other hand, y + 6 = 3 * (x + 6) gets you y + 6 = 3 * x + 18 which results in y = 3 * x + 12 and, since y = 4 * l, you get 4 * l = 3 * l + 12 which results in x = 12.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Let x be the Linda's current age (the unknown value under the question). Then Sarah's age is 4x, according to the condition. In 6 years, Linda's age will be (x+6) years; Sarah's age will be 4x+6 years. From the condition, 3*(x+6) = 4x + 6 Simplify and find x 3x + 18 = 4x + 6 18 - 6 = 4x - 3x 12 = x ANSWER. Linda is 12 years old now.

Solved.

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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 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 Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Sarah is currently four times as old as her daughter Linda.
in 6 years Sarah will be three time as old as Linda.
calculate Linda's current age.
--------------------
S = 4L
S+6 = 3(L+6) = 3L + 18
-----
4L + 6 = 3L + 18
L = 12
=======================
"currently" and "current" are superfluous.
There's no difference between age and "current age"
-----------
"What is your age?"
"What is your current age?"

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