Collection 3977

Tomáš brought the collection 20 percent less than Michal. Filip brought half of what Tomas did. Together, they brought 52.8 kg. How much did he bring?

Correct answer:

f =  9.6
m =  24
t =  19.2

Step-by-step explanation:


t = m - 20/100 m
f = t/2
t+m+f = 52.8

t = m - 20/100·m
f = t/2
t+m+f = 52.8

80m-100t = 0
2f-t = 0
f+m+t = 52.8

Pivot: Row 1 ↔ Row 2
2f-t = 0
80m-100t = 0
f+m+t = 52.8

Row 3 - 1/2 · Row 1 → Row 3
2f-t = 0
80m-100t = 0
m+1.5t = 52.8

Row 3 - 1/80 · Row 2 → Row 3
2f-t = 0
80m-100t = 0
2.75t = 52.8


t = 52.8/2.75 = 19.2
m = 0+100t/80 = 0+100 · 19.2/80 = 24
f = 0+t/2 = 0+19.2/2 = 9.6

f = 48/5 = 9.6
m = 24
t = 96/5 = 19.2

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