SOLUTION: barbara's age is 5 years less than her brother's age if her age is increased by 3 times her brother's age the result is 51 years find each of their age.

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Question 1070761: barbara's age is 5 years less than her brother's age if her age is increased by 3 times her brother's age the result is 51 years find each of their age.
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x, Barbara's age
y, Brother's age

x=y-5, her age is 3 times her brother's.
cross%283%28y-5%29%2By=51%29, three times her age and her brother's age, given as 51----------wrong interpretation;
-
If her age is increased by three times her brother's age
-should be x%2B3%28x%2B5%29;
-the result is 51
highlight_green%28x%2B3%28x%2B5%29=51%29--------this will give Barbara's correct age, x.



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The rest of this below is wrong
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SOLVE
3y-15%2By=51
2y=51%2B15
2y=66
highlight%28y=33%29
-
highlight%28x=28%29

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
barbara's age is 5 years less than her brother's age if her age is increased by 3 times her brother's age the result is 51 years
find each of their age.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The "josgarithmetic" solution is WRONG. 

Let "x" be the Barbara's age, "y" be her brother age.
Then 

x = y-5,       (1)
x + 3y = 51.   (2)

Substitute expression (1) into equation (2), replacing y. You will get

(y-5) + 3y = 51.

4y - 5 = 51  --->  4y = 51 + 5 = 56   --->  y = 56%2F4 = 14.


Thus the brother's age is 14 years. Then the Barbara's age is 14-5 = 9 years.

Answer.  Barbara is 9 years. Her brother is 14 years.

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
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".


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One notice at the end. The phrase
"Barbara's age is 5 years less than her brother's age."
doesn't sound harmonically/naturally in English. They say
"Barbara is 5 years younger than her brother."

Same for "find each of their age."



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
barbara's age is 5 years less than her brother's age if her age is increased by 3 times her brother's age the result is 51 years find each of their age.