First, calculate the total amount of hay consumed per day by 4 cows:
Daily consumption for 4 cows
=
63
kg
18
days
=
63
18
kg/day
=
3.5
kg/day
Daily consumption for 4 cows=
18 days
63 kg
=
18
63
kg/day=3.5 kg/day
Now, calculate how much hay one cow consumes per day:
Daily consumption per cow
=
3.5
kg/day
4
=
0.875
kg/day
Daily consumption per cow=
4
3.5 kg/day
=0.875 kg/day
Next, we need to find out how many cows will consume 770 kg of hay in 28 days at the same rate.
Calculate the total daily consumption needed for 770 kg of hay over 28 days:
Daily consumption for 770 kg in 28 days
=
770
kg
28
days
=
27.5
kg/day
Daily consumption for 770 kg in 28 days=
28 days
770 kg
=27.5 kg/day
Now, determine how many cows are needed to achieve this daily consumption rate:
Number of cows
=
27.5
kg/day
0.875
kg/day per cow
=
31.43
Number of cows=
0.875 kg/day per cow
27.5 kg/day
=31.43
Since we cannot have a fraction of a cow, we round up to the nearest whole number:
Number of cows
=
32
Number of cows=32
Therefore, 32 cows are needed to consume 770 kg of hay in 28 days at the same rate that 4 cows consume hay.
Answer:
To solve this problem, we need to determine the rate at which each cow consumes hay, and then use that rate to find out how many cows are needed to consume a given amount of hay over a specified period.
First, calculate the rate at which one cow consumes hay:
Given:
4 cows consume 63 kg of hay in 18 days.
Calculate the rate per cow per day:
Rate per cow per day= 63/4 cows×18 days
Rate per cow per day= 72/63/kg/day
Rate per cow per day=0.875 kg/dayNow, use this rate to find out how many cows are needed to consume 770 kg of hay in 28 days:
Let be the number of cows required.
x×0.875 kg/day×28 days=770 kg
Solve for x:
x×24.5 kg=770 kg
x= 770/24.5
x≈31.43
Since we can't have a fraction of a cow, we round up to the nearest whole number because we need at least this many cows to consume the hay within the specified time frame.
Therefore, 32cows are needed to consume 770 kg of hay in 28 days at the same rate as the initial scenario.