# Ticháček 7185

Mr. Ticháček had three gypsum dwarfs in the garden: the largest was called Maško, the middle Jarko, and the smallest Franko. Since he liked to play with them, he found out that when he puts Fan on Jarek, they are as tall as Maško. On the other hand, when they place Franko on Mašek, they measure 34 cm more than Jarko. And when they build on Mašek Jarek, they are 72 cm taller than Franko. How tall are dwarves
Mr. Ticháček?

f =  17
j =  36
m =  53

## Step-by-step explanation:

f+j=m
f+m = 34+j
m+j = 72+f

f+j-m = 0
f-j+m = 34
f-j-m = -72

Row 2 - Row 1 → Row 2
f+j-m = 0
-2j+2m = 34
f-j-m = -72

Row 3 - Row 1 → Row 3
f+j-m = 0
-2j+2m = 34
-2j = -72

Row 3 - Row 2 → Row 3
f+j-m = 0
-2j+2m = 34
-2m = -106

m = -106/-2 = 53
j = 34-2m/-2 = 34-2 · 53/-2 = 36
f = 0-j+m = 0-36+53 = 17

f = 17
j = 36
m = 53

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