Birthdate

Jane on birthday brought 30 lollipops and 24 chewing gum for their friends. How many friends has, if everyone receives the same number of lollipops and chewing gums? How much chewing gum and lollipops got any friend?

Correct answer:

x₁ =  6
y₁ =  5
z₁ =  4
x₂ =  3
y₂ =  10
z₂ =  8
x₃ =  2
y₃ =  15
z₃ =  12

Step-by-step explanation:

$$\begin{gathered} 30=2\cdot 3\cdot 5 \\ 24=2^3\cdot 3 \\ \text{GCD}(30,24)=2\cdot 3=6 \\ {x}_1=GCD(30,24)=6 \\ {d}_1=1 \\ {d}_2=2 \\ {d}_3=3 \\ {d}_4=6 \end{gathered}$$

$y_1=30\mathrm{/}{x}_1=30\mathrm{/}6=5$

$z_1=24\mathrm{/}{x}_1=24\mathrm{/}6=4$

$x_2=3$

$y_2=30\mathrm{/}{x}_2=30\mathrm{/}3=10$

$z_2=24\mathrm{/}{x}_2=24\mathrm{/}3=8$

$x_3=2$

$y_3=30\mathrm{/}{x}_3=30\mathrm{/}2=15$

$z_3=24\mathrm{/}{x}_3=24\mathrm{/}2=12$

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