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Age Problem Differences

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by jnellaz » Wed Nov 19, 2008 7:13 pm
Can someone assist with the following two problems? According to the text, Problem 1 only has one unknown while Problem 2 has two unknowns. Thus the approaches were different. To me, I can't tell the difference. Could someone explain how they would approach these problems and whether your approach for each would have one unknown or two? Thanks!

Problem 1:
Sid is twice as old as Rex. Ten years ago, Sid was four times as old as Rex. How old is Sid today?

[spoiler]Answer: 30[/spoiler]


Problem 2:
Joan is 4 times the age of Ben. In 4 years, Joan will be 2.5 times the age of Ben. Ben will be how many years old ten?


[spoiler]Answer: 8[/spoiler]
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by cramya » Wed Nov 19, 2008 7:24 pm
I would solve with just 1 variable for both. Please see attachment.

Hope this helps and let me know if u still have questions.
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by jnellaz » Wed Nov 19, 2008 7:46 pm
Thank you very much, Cramya!
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by rmpaes » Wed Nov 19, 2008 7:51 pm
Sid is twice as old as Rex. Ten years ago, Sid was four times as old as Rex. How old is Sid today?
Let S = Sid's age
Let R = Rex's age

we can get 2 equations by translating the English into math:
now:
(i)S = 2R
ten years ago:
(ii)S-10=4(R-10)

i)S = 2R
ii)S = 4R - 40 +10 [manipulate eq ii]



2R = 4R - 30 [substitute S= 2R into eq ii]
2R = 30
R = 15
i)S = 2(15) = 30
Joan is 4 times the age of Ben. In 4 years, Joan will be 2.5 times the age of Ben. Ben will be how many years old then?
Let J = Joan's age
Let B = Ben's age

now:
(i) J = 4B

four years in future:
(ii) J + 4 = 2.5(B + 4)

2J + 8 = 5(B + 4) [multiply eq ii by 2]

8B + 8 = 5B + 20 [substitute J=4B into eq ii]
3B = 12
B = 4
We want to know Ben's age in 4 years
B+ 4 = 8
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Re: Age Problem Differences

by logitech » Wed Nov 19, 2008 8:10 pm
A = 3 years old

B = 7 years old

So B is 4 years older than A

what happens in 5 years ?

A = 3 + 5

B = 7 + 5

B is still 4 years than A.

This sounds silly right ? This is where most of the people make mistakes in ages question.


Now the sum of their age is 3+7 = 10

how about in 5 years ?

10 + 2x(5) = 20

how about 2 years ago

10 - 2x(2) = 6

Take away:

The difference between people's age does not change over the time!

And two people in X years , will have 2X years of addition to their age's sum.
LGTCH
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by jnellaz » Thu Nov 20, 2008 6:52 am
Rmpaes, thanks again for your approach!
Logitech, as always...great insight! You're the man, behind the man!
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