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To determine the cost of the boxes with given base areas, we'll first calculate their volumes and then use the price per cubic inch to find the costs.

Volume Calculation
The volume of a cuboid is given by:
Volume=Length×Width×Height

Since the length and height are given as 6 inches and 9 inches respectively, we can use the base area to find the width.

For the box with a base area of 24.5 square inches:
Base Area=Length×Width

24.5=6×Width
Width= 24.5/6 ≈4.0833 inches

Now, calculate the volume:
Volume=6×4.0833×9

Volume=220.5 cubic inches

For the box with a base area of 32.75 square inches:
Base Area=Length×Width

32.75=6×Width
Width= 32.75/6 ≈5.4583 inches

Now, calculate the volume:
Volume=6×5.4583×9
Volume=295.5 cubic inches

Cost Calculation
The cost per cubic inch is $2. Hence, the cost of each box is given by:
Cost=Volume×2

Cost of the box with a base area of 24.5 square inches:
Cost=220.5×2=441

Cost of the box with a base area of 32.75 square inches:
Cost=295.5×2=591

Closest values in the table:
Base area 24.5 square inches: $440 (closest to $441)
Base area 32.75 square inches: $590 (closest to $591)

Therefore, the selections are:
Base area 24.5 square inches: $440
Base area 32.75 square inches: $590
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Cost is proportional to width
width is proportional to base area
ratio of costs= 24.5/32.75=0.75 approx

if Cost of 24.5 sq inch is C1, Cost of 32.75 sq inch will be 4C1/3

choose options with ratio closest to 3/4 or select options in ascending order and find 4C/3 and look for 2nd match

Only (440,586) is the closest

Hence 440, 590 (C,E)
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Bunuel
­A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.


­
 


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Since ­The boxes are both 6 inches long and 9 inches high but differ in width and The base area of a cuboid is length x width.
=> width of one box of base area 24.5 square inches = 6 x w => w = 24.5 / 6 = 4.083
=> width of one box of base area 32.75 square inches = 6 x w => w = 32.75 / 6 = 5.4583 

The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.
=> cost of one box of base area 24.5 square inches = 6 x 4.083 x 9 x 2 = 441 dollars => choose $440 
=> cost of one box of base area 32.75 square inches = 6 x 5.4583 x 9 x 2 = 589.5 dollars => choose $590 
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Base area 24.5 square inches: 440
Base area 32.75 square inches: 590

­Price of box: 9*2*base area

24,5base: 18*24,5 is rounded up 18$25= 450
the answer should be a bit less
32,75 base: 18*32,75= 18*30+3*18= 540+54=594
the answer should be a bit less
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We have to find cost of each box that goes by price per volume
Constructing the equation, when we put volume along
(L*W*H)*price

But we are already have the base of boxes (which is L*W) as 24.5 and 32.75

Multiply each base with height (9" as per data) so arrive at volume

Box 1: 24.5*9 = 220.5
Box 2: 32.75*9 = 294.75

Multiply volume with 2 gives us cost of

24.5 box: 220.5*2 = 441 or ~440

32.75 box: 294.75*2 = 589.5 or ~590

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IMO - Base area 24.5 square inches - $440

Base area 32.75 square inches - $590


Volume - l x w x h

Base area already has l x w - Just multiply by height and $2 to get the value.

As numbers are far apart just do the approximation

24.5 * 9 * 2 = 25*18 = (50/2)* 18 = around 450$

Similarly for other number

32.75*9*2 = 30 * 18 = around 540$
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Base area 24.5 square inches:24.5*9*2=441=approx $440
Base area 32.75 square inches: 32.75*9*2=589.5= approx $590
Ans C, E
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­A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.

l*w given 24.5 square inches & 32.75 square inches

value of l* w 24 .5 *2*9 = 441 ~ 440
value of 32.75*2*9 = 589.5 ~ 590

correct option Base area 24.5 square inches $440 & Base area 32.75 square inches $590
440 & 590
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­A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.

Volume of cuboid = length x width x height = Base Area * Height = Base area * 9
Price of one box = 2*Volume = 2*9*Base Area = $18*Base Area


The cost of one box of base area 24.5 square inches = 18*24.5 = 441 = $440 Approx

The cost of one box of base area 32.75 square inches = 18*32.75 = 589.5 = $590 Approx
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Bunuel
­A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.


­
 


This question was provided by Experts' Global
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­
­Value for 24.5 sq inch face area = 24.5*9*2= 441

Value for 32.75 sq inch face area = 32.75*9*2 = 589.5

IMO 440 and 590
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Base area 24.5 , volume=24.5*9=220.5, price= $2*220.5=$441
Base are 32.75
Volume=32.75*9=294.75, price=
$2*294.75=589.5

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Volume of first box = 24.5*9 = 220.5 cubic inches
then, cost of first box = 220.5*2 = $441 ~ $440

Volume of second box = 32.75*9 = 294.75 cubic inches
then, cost of second box = 294.75*2 = $589.5 ~ $590
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­A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.

Explanation:
base area = length * width
volume = length * height * width = base area * height = base area * 9
(height is 9 inches for both boxes)

Cost of cuboidal box = volume * $2 = base area * height * $2 = base area * 9 * $2

Box with 24.5 sq. inches base area
Cost of box = 24.5*9*$2 = 441 = $440

Box with 32.75 sq. inches base area
Cost of box = 32.75*9*$2 = 589.5 = $590
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­Given That, 
  •   The boxes are both 6 inches long and 9 inches high but differ in width. 
  •   The boxes are priced by volume at $2 per cubic inch
  •   The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. 
Base area = Length*width 

w1= Base area / length , 
w1= 24.5/6= 4.08 , similary w2= 5.46

V1(24.5) = L*H*W1*2 = 432.96
v2(32.75) = 598. 


From table, we can analsise that v1 = 440 & v2= 590
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Bunuel
­A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.


­
 


This question was provided by Experts' Global
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­
­Multiply Base area by Height *2 so you will get values 440.5 for 24.5 square inches and 589.5 for 32.75 square inches respectively.
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­l=6
b=9
w=w
A=24.5 square inches
W=A/l=
4
V=6*9*4=220
Cost =220*2=440
A=32.75 square inches
W=A/l=5.5
V=6*9*5.5=270
Cost =270*2=590
Ans CE

 
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Bunuel
­A retailer needs to purchase cuboidal boxes of two different sizes. The boxes are both 6 inches long and 9 inches high but differ in width. The boxes are priced by volume at $2 per cubic inch. The volume of a cuboid is length x width x height.

The base area of a cuboid is length x width. In the table below, select the value that is closest to the cost of one box of base area 24.5 square inches as well as the cost of one box of base area 32.75 square inches. Make only one selection in each column.


­
 


This question was provided by Experts' Global
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­
­Box 1: Volume = 24.5*9 = ~221
Box 2: Volume = 32.75*9 = ~295

Box 1: Cost = 2*221 = $441
Box 2: Cost = 2*295 = $590

Therefore, option (3) and (5) in the first and second column respectively.
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