My 5th grader is practicing simple arithmatic fractions. He stumbled upon a question and now its troubling me too. I can't seem to solve the question without the help of Algebra which I can not explain to my kid without a proper introduction. Will appreciate if someone can give a hint on solving it without involving Algebraic expressions. Question goes as follows:
Peter, John and Mary share 78 marbles. Peter takes $\dfrac{1}{3}$ of the marbles and John takes thrice as many as Mary. Find the number of marbles John takes.
Edit: Apparently the question has been marked-down due to the absence of my attempt. So here it goes:
$\dfrac{1}{3}$ of 78 is 26. So Peter took 26 away from 78. 52 remains to distributed among John and Mary. From the given info John (J) keeps 3 times of the Mary's(M) share so J=3M. We know J + M = 52. We can substitute J in the equation that will become 3M + M = 52, therefore M = $52 \div 4$ $\implies$ M = 13. As J=3M, therefore J = $3\times 13$ which is 39. But this involves Algebra which I want to avoid explaining my kid at this moment.
To a 5th grader who cannot make algebraic equation, you can explain in steps -
There is a nice one you can try to explain to a 5th grader without algebraic equations:
There are total of 45 soldiers and horses. If there are 120 legs in total, how many soldiers and horses?