Maths-
General
Easy
Question
8 bags of cattle feed are needed to feed 4 cows for 2 months. How long will the same feed last to feed 6 cows?
Hint:
Hint:
In a proportional relationship, the variables are related by a constant ratio(k). For example, the equation which can relate the two variables can be written in the form:
y = (constant) x or y = k x.
So, for solving these types of questions we need to create a proportional relationship between the variables. These relationships can be direct, inverse etc.
The correct answer is: Hence, the small feed will last for 1 1/3 to feed 6 cows.
Let the number of bags of cattle be represented as x, the number of cows be represented as y and the number of months be represented as z. Now, more cows will mean more bags of cattle are required so x and y will have a directly proportional relationship i.e
y
x
Now if there are more cows this means the bags of cattle will last for fewer months which means x and z have an inversely proportional relationship i.e
y
![1 over z](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAHRJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CkYBXUA9jgRYTqnBkkB8EIhFKTFEEIh3A7E0JYZwAPEmINah1EvLgdiWUkOmAbEPpYZUAnE8pYZEUiOaQeADjjTEhksDAIxaMWzTsWGKAAAAYnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MTwvbW4+PG1pPno8L21pPjwvbWZyYWM+PC9tYXRoPrMGA88AAAAASUVORK5CYII=)
So, we can say that
y
![x over z](data:image/png;base64,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)
y =
…….(1)
Where k is a proportionality constant
Step 1 of 2:
It is given that 8 bags of cattle feed are needed to feed 4 cows for 2 months. So, x = 8, y = 4 and z = 2. Putting the values in equation (1)
4 = ![k 8 over 2](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAAjCAYAAACHIWrsAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAXNJREFUeNpjYKAccAHxJCD+AsQ/gHgHEEsz0BDMBeJWIGYBYjYg7gDik7S08AcanwmIf9HSQlBQ8qBZ+JiWFoLiLw+JbwnEPbS0UA8ahCB8EIifA7EtrSyTB+KlQCwJTTAgYAzEd6EOoTpYh8NgRyDeT48USqwc2eAaEKtgEdeCxiXVQRDUUkdodmCCskFxmEGMAd+gmkgBoUB8DppKf0BTagAxGkFBc4mBjgDkquX0tLAeiMuhbFBBvBCIvWhp4SqoLzmgbEda+/AWEOsA8SYgNqe1ZUzQFHocaik+8J9MjALMoUVRJLRCpTkAWTQfyu4hNtNSWqelIfF3A7E1LS1ch5YFBKHtEklaWfgOmh2QASjx7MUiPqAAFOxrgPgTtCy9AMTRtLTwIDTB8SBVS0ehYnQD8vSuBGhW2+MCltBgpQvggGYna3pYBsq7G4DYjR6WKUEtU6GHZRpAPBvabaM5EIdW1iz0SiRboD6kGyC6woUBAHmaVm1ZvluAAAAAbHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5rPC9taT48bWZyYWM+PG1uPjg8L21uPjxtbj4yPC9tbj48L21mcmFjPjwvbWF0aD4oQdWlAAAAAElFTkSuQmCC)
k =
= 1
Step 2 of 2:
Now we are asked to find the number of months the same feed will last to feed 6 cows. So, x = 8, y = 6 and we need to find z. Putting the values in equation (1)
6 = ![k 8 over z](data:image/png;base64,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)
Now, put the value of k = 1
z = ![1 cross times 8 over 6](data:image/png;base64,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)
d =
=
months
Final Answer:
Hence, the small feed will last for
to feed 6 cows.
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Maths-
Approximate the following irrational numbers to the nearest whole number. ![negative square root of 39](data:image/png;base64,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)
Approximate the following irrational numbers to the nearest whole number. ![negative square root of 39](data:image/png;base64,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)
Maths-General
Maths-
A car needs 33 litres of petrol to cover a distance of 363 km. Petrol costs · 78 per litre. How much would one spend on a journey of 407 km by car?
A car needs 33 litres of petrol to cover a distance of 363 km. Petrol costs · 78 per litre. How much would one spend on a journey of 407 km by car?
Maths-General