Birthdate

Jane brought 30 lollipops and 24 chewing gum for their friends on her birthday. How many friends does she have if everyone receives the same number of lollipops and chewing gums? How much chewing gum and lollipops have any friends?

Correct answer:

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

Step-by-step explanation:

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

$y_1=30/x_1=30/6=5$

$z_1=24/x_1=24/6=4$

$$\begin{gathered} ---------------- \\ {x}_2=3 \end{gathered}$$

$y_2=30/x_2=30/3=10$

$z_2=24/x_2=24/3=8$

$$\begin{gathered} ---------------- \\ {x}_3=2 \end{gathered}$$

$y_3=30/x_3=30/2=15$

$z_3=24/x_3=24/2=12$

Try another example