Shoes

Peter decided to measure the shoe size of his three friends. Measured accurately and written as follows:

Venda and Jenda together 52 cm
Jenda and Zdenda together 58 cm
Zdenda and Venda together 54 cm
a) How long measure Vendy, Jenda, and Zdenda shoes together?
b) Determine the length of each shoe individually

Correct answer:

s =  82 cm
v =  24 cm
j =  28 cm
z =  30 cm

Step-by-step explanation:

$$\begin{gathered} a=52\text{cm} \\ b=58\text{cm} \\ c=54\text{cm} \\ v+j=a \\ j+z=b \\ z+v=c \\ v+j=52 \\ j+z=58 \\ z+v=54 \\ j+v=52 \\ j+z=58 \\ v+z=54 \\ Row2-Row1\to Row2 \\ j+v=52 \\ -v+z=6 \\ v+z=54 \\ Row3+Row2\to Row3 \\ j+v=52 \\ -v+z=6 \\ 2z=60 \\ z=\frac{60}{2}=30 \\ v=\frac{6-z}{-1}=\frac{6-30}{-1}=24 \\ j=52-v=52-24=28 \\ j=28 \\ v=24 \\ z=30 \\ s=v+j+z=24+28+30=82\text{cm} \end{gathered}$$

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