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Zadanie17

Within four weeks, 12 cows eat the grass of the meadow with an area of \u200b\u200b313



jugiera. We assume that during this whole time the grass is growing steadily. Within nine weeks 21
cow eats the grass of the meadow area of \u200b\u200b10 jugierów. How many cows eat grass from a meadow
jugierów surface 24 within 18 weeks?





solution to the problem
Let x is the amount of grass on the surface of one jugiela, and y is the amount of growth may
new grass on the surface of one jugiera within one week. Then, on the surface
313
jugiera is
103x
grass, and stirred for four weeks on the pasture grows

4,103 's

grass. From this it follows that a cow eats in a week



4103 y
103 x 4.12



grass.

the other hand, the amount of grass in a meadow with an area equal to 10 jugierów is 10x, and within nine weeks of
meadow grass grows 90Y. One cow in a week so eats



90Y 10 x 9.21



grass.



get the equation



403y
103 x
4.12



90Y = 10 x 9.21



Hence 9 · 21 ·
103
(4y + x) = 4 ⋅ 12 * 10 (9Y + x).


get x = 12Y


One cow eats in a week
109Y
grass.

amount of grass for 24 jugierach equals 24x = 24 ° 12 · y


Within 18 weeks on the meadow grows 24 ° 18 's grass.
total amount of grass, which is enough for 18 weeks equals 24 ° 12
's + 24 ° 18' s = 24 ° 30 ° y


Within 18 weeks a cow eats
109Y
· 18 = 20Y grass.

Grass is therefore sufficient for


24.30
20Y y = 36 cows.