Homework - jumps

Sasha jumped 131 cm Peter 4 cm more than Jirka.
Jirka 6 cm less than Misha. Misha 7 cm less than Filip, and Filip is half as much as Sasha and Petr together. How far does each jump?

Correct answer:

S =  131 cm
P =  113 cm
J =  109 cm
M =  115 cm
F =  122 cm

Step-by-step explanation:

$S=131=131\text{cm}$

$$\begin{gathered} P=4+J \\ J=M-6 \\ M=F-7 \\ F=(S+P)/2 \\ F=(S+P)/2=(4+J+S)/2=(4+M-6+S)/2=(4+F-7-6+S)/2 \\ F=(4+F-7-6+S)/2 \\ 2F=4+F-7-6+S \\ F=4-7-6+S=4-7-6+131=122\text{cm} \\ M=F-7=122-7=115\text{cm} \\ J=M-6=115-6=109\text{cm} \\ P=4+J=4+109=113\text{cm} \end{gathered}$$

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