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### Age and Money

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Date: Tue, 13 Dec 1994 18:38:36 AST
Comments: NB*net - New Brunswick's Regional Network
1-800-561-4459
From: Richard Seguin

Could you help me solve this. I am a grade 9 student.

1> Frank is eight years older than his sister. In three years he will be
twice as old as she is. How old are they now?

2> Karen is twice as old as Lori. Three years from now the sum of
their ages will be 42. How old is Karen?

3> Dave has six times as much money as Fred, and bill has three times
as much money as Fred. Together they have 550.00. How much does
each have?

4> To find the length of a certain rectangle you must triple the width and
add 5m. If the perimeter of the rectangle is 74m, find the dimensions.

I hope you can help me solve these. I had no luck!

Richard
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Date: Wed, 14 Dec 1994 09:53:08 -0500 (EST)
From: Dr. Sydney
Subject: Re: Grade 9 (Richard Seguin)

Dear Richard,

Thanks for writing Dr. Math.  These word problems can get a
little confusing, but usually things work out if you assign all of your
unknowns a letter name and write the information down in an equation.
Let's try the first one...

1) The first thing to figure out is what you are trying to figure out.
In the first problem, we want to know Frank's age and his sister's age.
The next thing to do is assign letters to unknowns.  Let's call Frank's
current age f, and let's call Frank's sister's current age s.  Now let's
translate what the sentences in the problem say to mathematical
equations.

a) "Frank is 8 years older than his sister."  This means if we add 8 to
Frank's sister's age we would get Frank's age, right?  So, we have:

s + 8 = f

b) "In three years he will be twice as old as she is."  In three years,
Frank will be three years older than he is now, so he'll be f+3 years old.
Similarly, his sister will be s+3 years old.  At that time, he will be twice
as old as she is, so if we were to multiply Frank's sister's age in three
years by 2, we would get Frank's age in three years.  So, we have:

2 (s + 3) = f + 3

So, now we have a systems of equations -- 2 equations, 2 unknowns.
Simplify these and solve:

2s + 6 = f + 3

So,     f = 2s + 3

Substituting this in the first equation, we get:

s + 8 = 2s + 3

Simplify to get:

s = 5

If s = 5, then what must f be?  Plug into either equation to
get: f = 13.  So, Frank's sister's age is 5 and Frank's age is 13.  You
in the problem.  Check that Frank is 8 years older than his sister:
13 is 8 more than 5, so this does make sense.  Now check that in three
years he will be twice as old as she is.  In three years they will be 16
and 8 years old.  16 is 2 times 8, so this works.  So, we did everything
right.  Did that make sense to you?

I bet now you can do some more of these problems.  Mainly they
involve translating the sentences into math equations.  If you have any
more problems or are confused by anything I said, please feel free to
write back.

--Sydney
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Associated Topics:
Middle School Word Problems

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