Shoes

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

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

Final Answer:

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

Step-by-step explanation:

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

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