# 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?

Result

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

#### Solution:

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

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