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the sides of the smallest box are 30% of the length of the sides of the largest box. the volume of the largest box is 7784 cubic inches more than the volume of the smallest box. let x represent the length of the side of the largest box. write an equation that represents the difference in the volume of the two boxes.



Answer :

The length of the side of the smaller box is 6 and the length of the side of the larger box is 20. The equation for the difference in volume of the boxes is, y3 - x3 = 7784 .

Let us consider the length of side of small box be x inch & length of large box be y inch.

Length of smallest box is 30% of the length of the side of the largest box 

x=30%*y

   = 30 * y / 100

x = 3y / 10

Volume of the smallest box is x3.

volume of the largest box is y3.

Volume of largest box is 7784 cubic inches more than the volume of smallest box. Therefore,

y3 =  x3 + 7784

     = (3y/ 10 )3 + 7784

     = 27y3 / 1000 + 7784

y3 - 27y3 / 1000 = 7784

973 y3  / 1000 = 7784

973 y3 = 7784 * 1000

y3 = 7784 * 1000 / 973

y3 = 8000

   y = 20

Now find the smaller side.

x = 3y / 10

putting the value of y  this we get,

x = 3 * 20 / 10

   x= 6    

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