Homework - jumps

Sasha jumped 121 cm Peter 4 cm more than Jirka.
Jirka 6 cm less than Misha. Misha 7 cm less than Filip and Filip half as much Sasha and Petr together. How far each jumped?

Correct answer:

Saša:  121 cm
Petr:  103 cm
Jirka:  99 cm
Míša:  105 cm
Filip:  112 cm

Step-by-step explanation:

Petr#cm=4 + 4-7-6+121 - 7 - 6=103 \ \text{cm}

Jirka#cm=4-7-6+121 - 7 - 6=99 \ \text{cm}

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$$\begin{gathered} S=121 \\ P=4+J \\ J=M-6 \\ M=F-7 \\ F=(S+P)\mathrm{/}2 \\ F=(S+P)\mathrm{/}2=(4+J+S)\mathrm{/}2=(4+M-6+S)\mathrm{/}2=(4+F-7-6+S)\mathrm{/}2 \\ F=(4+F-7-6+S)\mathrm{/}2 \\ 2F=4+F-7-6+S \\ F=4-7-6+121=112\text{ cm } \\ M=F-7=105cm \\ J=M-6=99cm \\ P=4+J=103cm \end{gathered}$$

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