On Children's

On Children's Day, the organizers bought 252 chewing gums, 396 candies and 108 lollipops. They want to make as many of the same packages as possible. Advise them what to put in each package and how many packages they can make this way.

Correct answer:

z =  2
b =  3
l =  1
n =  108

Step-by-step explanation:

$$\begin{gathered} 252=2^2\cdot 3^2\cdot 7 \\ 396=2^2\cdot 3^2\cdot 11 \\ 108=2^2\cdot 3^3 \\ \text{GCD}(252,396,108)=2^2\cdot 3^2=36 \\ d=GCD(252,396,108)=36 \\ n=min(252,396,108)=108 \\ z=\lfloor 252\mathrm{/}n\rfloor =\lfloor 252\mathrm{/}108\rfloor =2 \end{gathered}$$

$b=\lfloor 396\mathrm{/}n\rfloor =\lfloor 396\mathrm{/}108\rfloor =3$

$l=\lfloor 108\mathrm{/}n\rfloor =\lfloor 108\mathrm{/}108\rfloor =1$

$$\begin{gathered} n=108 \\ \text{ Verifying Solution: } \\ {z}_1=252-n\cdot z=252-108\cdot 2=36 \\ {z}_2=396-n\cdot b=396-108\cdot 3=72 \\ {z}_3=108-n\cdot l=108-108\cdot 1=0 \end{gathered}$$

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