# Question

hi, need help for this sum

Mr Gopal donated1/6 of his money plus \$12 to the red Cross society. he spent 2/3 of the remaining money and an additional \$26 on a meal. he had \$83 left. how much money did he have at first?

If a branch diagram helps.

Step 1:  Branch out a diagram and write down information:

All money (           )

Donate 1/6 +\$12 (     )                          Remainder 5/6\$12(       )

Meal 2/3 +\$26 spent (     )          Left (\$83)

Step 2:  Think for a “convenient” number of u (LCM of 6 and 3 is 18u – in error. Should be “convenient set” of u is 18u, explained in my later post below.)

Step 3:  Input the no. of units.,  analyse the branch diagram… and Solve

All money (#1. 18u)

Donate 1/6+\$12 (#2. 3u+12)                    Remainder 5/6-\$12( #3. 15u-12)

Meal 2/3 +\$26 (#4. 10u-8+26)   Left (\$83)(#5.=5u-4-26)

See #5.   83 = 5u-4-26 –> u=22.60

At first = 18u = \$406.80#

Alternatively, work backwards (the 1st branch diagram above can help analyse the below too):

If the \$26 is taken from the Meal and added to the Leftover money = \$83+\$26 = \$109

\$109 is 1/3 of Remainder (1 part) –> \$327 is the Remainder (3 parts)

If the \$12 is taken from the Donation and added to the Remainder = \$327+\$12 = \$339

\$339 is 5/6 of the Total  (5 units) –> \$406.80# is the Total amount of money (6 units)

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The lcm of 6 & 3 is 12 i think. Then y 18 is taken as lcm

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Updated 10/5/2017 2:19pm – Hi naguruji, yes, you are correct. Mathematical LCM of 6 and 3 is 6. I’m mathematically wrong earlier. I used 18u earlier in above working, because:

After getting units for 5/6, I must be able to divide the numerator 5 parts into 3.

If I use 6u, I get 5u in 5/6, which is inconvenient to be divided into 3.

If I use 12u, I get 10u in 5/6, which also is inconvenient to be divided into 3.

If I use 18u, I get 12u in 5/6, which can be conveniently divided into 3. So I shall be corrected to say that a convenient unit to use is 6 x 3 = 18u. Corrected in above original working above. Thanks for pointing out.

Rest assure that even if inconvenient no. of units is chosen, it can still work as shown in below reworked example using 6p.

Below for illustration only:

Step 2:  Think for a “convenient” number of u (Mathematical LCM of 6 and 3 is 6p – corrected, but not so convenient below)

Step 3:  Input the no. of units.,  analyse the branch diagram… and Solve

All money (#1. 6p)

Donate 1/6+\$12 (#2. 6p+12)                    Remainder 5/6-\$12( #3. 5p-12)

Meal 2/3 +\$26 (#4. 10p/3-8+26)   Left (\$83)(#5.=5p/3-4-26)

See #5.   83 = 5p/3-4-26 –> p=67.80

At first = 6p = \$406.80#

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In this case it is not about lcm. it is about multiplying 6 and 3 to get 18. Afterall, lcm of 6 and 3 is 6.

Why 18? because there’s 5/6 term, upon which we are multiplying with another 2/3. So the denominator will have 18. If you do algebra assuming the original amount as x, you can see that you will be multiplying 5/6 x with 2/3, which gives you 10/18 x, which correspond to the 10u in the diagram by SAHMom.

Hi dryu, thanks for explaining. our posts crossed while I updated this solution. Cheers!

No worries SAHMom. I think you give a very detailed illustration and good branching method. Sometimes it is really tricky for kids to figure out what is the convenient coefficient of u, and if a wrong number is chosen (as you illustrated), they will need to deal with fraction, which generally is less ideal. Anyway, I usually prefer to work backwards for this type of questions. Easier for kids to understand. 🙂

Agree absolutely. That’s why so many methods for 1 question. Yes, I also begin to see the beauty of working backwards too, especially dealing with things like “additional \$26” or “spent 1/4 and \$5 less” and the more layering of info nowadays. Maybe that’s why I seldom use this branching method of convenient “u” nowadays. Though I still view a branch diagram a good visual tool for using with working backwards.  Below is a link for what I meant, for interest only.

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SAHM, thanks for all your examples of the branching method!  I think it works better than drawing models for many of the questions.

Thanks, as long as it helps for some who prefer this, I’d glad. Cheers.

Also this new platform is much easier to edit and format than the previous one.

I just went back to my earlier posts to copy my branch diagram and edit and viola, it’s all done! 🙂

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Working backwards,

1 – (2/3) = 1/3

83 + 26 = 109 (1/3 of remaining money)

109 x 3 = 327 (the remaining money)

1 – (1/6) = 5/6

327 + 12 = 339 (5/6 of his money)

(339/5) x 6 = 406.80

Ans : 406.80.

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