
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?

Chatty
Registered: 02/28/12 Posts: 68





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 unit10 / 2 = 5
Ronald  4units x 5 = 20 yrs old(now)
Hope this clear enough.

Regular Member
Registered: 11/07/10 Posts: 70





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.

Chatty
Registered: 02/28/12 Posts: 68





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

Regular Member
Registered: 11/07/10 Posts: 70





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.
Thank you

Chatty
Registered: 02/28/12 Posts: 68





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

Active Member
Registered: 04/21/11 Posts: 623





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.

Regular Member
Registered: 11/07/10 Posts: 70



