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68 boxes of certain commodity require a shelf-length of 13.6 m. How many boxes of the same commodity would occupy a shelf length of 20.4m?

Answer:

Let’s consider number of boxes as ‘x’

13.6/68 = 20.4/x

By cross-multiplying

13.6x = 20.4(68)

13.6x = 1387.2

x = 1387.2/13.6

= 102

∴ Number of boxes are 102

"Hello, dear student. I'm Sunita Nia from Ledo learning. I am here to help you solve the problem, which goes like this 68 boxes. Of a certain commodity require a shelf length of 36 thirteen point six meters how many boxes of the same commodity would occupy a shelf length of 20 point four meters? So let's put these values down in the table that I have prepared.
Here I will write.
Shelf length
In meters
And below that I will write number of boxes.
So now you can see that these boxes are arranged as you as the picture indicates. So, let's see if the Shelf length is 13 point 6 meters. The number of boxes it can accommodate is 68 Now if the Shelf length is increased to twenty point four meters. We need to find how many boxes it can accommodate. So let that number be X now. We know that if the Shelf length is increased the number of boxes. It can accommodate will also increase. So this is a case of direct variation as a shelf length increases. The number of boxes will also increase
So in the case of direct variation, the constant of variation is given by
Is given by the ratio of the two quantities, that is 13.6. / 68 this is the constant of proportionality or variation. Now this constant given by 13.6 upon 68 is also given by the ratio of 20.4 to Nava. Unknown X Now by cross multiplying we will get 13 point 6 into X is equal to 20. .4. X 68 or our unknown X is equal to twenty point four. In 268 X 13.6 let's reduce this we can get rid of the decimal point and we shall reduce with to
68 and then here 30 home.
In fact that the full ones are 34 and 34 tools are 68 and to be canceled with 204 to give 102. So we find our unknown X to be 102 Boxes
So our answer is hundred and two boxes. I hope you understood this Solution. Please do add comments in the comment section, and if this video has helped you to visit our Channel regularly for more boom box Solutions being explained to you. You can subscribe to it for updates as well. Thank you."

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