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 Maths Questions 14
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By: shirley wee (offline)  Friday, June 29 2012 @ 06:37 AM CDT (Read 1593 times)  
shirley wee

Hi everybody! I am stuck with this Maths Question. Please help me to solve it and show the workings clearly.

Mark's current age is 1/4 of Ronald's. In 24 years' time, Ronald's age will be 14 years less than twice Mark's age. What is Ronald's age now?

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By: GIM (offline)  Friday, June 29 2012 @ 07:11 AM CDT  
GIM

Now,
M [--1u--]
R [--1u--][--1u--][--1u--][--1u--]
|||||------------4units--------------|

In 24yrs,
|||||<-------------Mark------------>|<------------Mark--------------->|
M [------------24-----------][--1u--][--1u--][------------24------------]
R [------------24-----------][--1u--][--1u--][--1u--][--1u--]-14less-|
||||<add 24yrs to each>|<------------4units----------->|

2 units ----- 24 -14 = 10
1 unit--------10 / 2 = 5
Ronald ----- 4units x 5 = 20 yrs old(now)

Hope this clear enough.

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By: shirley wee (offline)  Friday, June 29 2012 @ 07:30 AM CDT  
shirley wee

But the answer sheet that was given by my teacher wrote '20 years old'. Can you help me to qualify is it the answer sheet has any mistakes? I am very confused. Confused

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By: GIM (offline)  Friday, June 29 2012 @ 08:11 AM CDT  
GIM

Sorry I made a mistake!

M [---------24---------][------][------][----------24----------]

R [---------24---------][------][------][------][------]14less|

2 units -----> 24 -14 =10
1 unit ------> 10 / 2 = 5
Ronald ----> 4 units x 5 = 20 yrs old

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By: shirley wee (offline)  Friday, June 29 2012 @ 09:32 AM CDT  
shirley wee

Can you explain clearly why Mark's age is not 1/4 of Ronald's? I still do not understand your model. Frown
Thank you

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By: echeewh (offline)  Friday, June 29 2012 @ 06:49 PM CDT  
echeewh

Hey Shirley

The model shown by GIM is the <After> model.

M: 2u + 48 ( given that M's age is doubled )
R: 4u + 24

And you are given that M - R = 14

Hence, if you work backwards,

M: 1u + 24
R: 4u + 24

These are the ages in 24 yrs time. Hence, current ages are as follows:

M: 1u
R: 4u

Now, M's age is 1/4 that of R's.


An alternative method to GIM's method (without model) is as follows:

<Now>

M: 1u
R: 4u

<in 24 yrs time>

M: 1u + 24
R: 4u + 24

Given that Ronald's (R) age will be 14 years less than twice Mark's (M) age, we have ...

2M - R = 14 or 2M = 14 + R
2 (1u + 24) = 14 + 4u + 24
2u + 48 = 4u + 38
4u - 2u --> 48 - 38
2u --> 10
1u --> 5

R's age now = 4u --> 4 x 5 = 20 yrs old

=======================================

Trust the above helps.

Cheers,
Edward

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By: GIM (offline)  Sunday, July 01 2012 @ 02:33 AM CDT  
GIM

I have edited my first solution, hope the solution is clearer to you now.

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