Alex A.

asked • 09/14/15# Please answer this word problem! With solutions and explanation would be very much appreciated. Thank you!

## 3 Answers By Expert Tutors

Conor R. answered • 09/14/15

Math and Physics specialist.

**h**be the height,

**l**the length,

**w**the width, and

**V**the volume.

**h = 2l**

**l = 2w**

*note that you may substitute*

*the second equation into the first to get:*

**h = 2(2w) = 4w**

**cubic**inches). We will use

**V**as the box's

*original volume.*You should already know that the volume of a box is described by the equation

**V = lwh**. To transform this sentence to an equation, simply add 1 to each dimension and 71 to the total volume:

**(l+1)(w+1)(h+1) = V+71 = lwh+71**

**w**.

**(2w+1)(w+1)(4w+1) = (2w)(w)(4w)+71 = 8w**

^{3}+71**8w**

^{3}+14w^{2}+7w+1 = 8w^{3}+71

**14w**

^{2}+7w-70 = 0**7(2w**

^{2}+w-10) = 7(w-2)(2w+5) = 0**w-2 = 0**or

**2w+5 = 0**. Solving those two equations gives us

**w = 2**or

**w = -5/2**

*.*We can safely throw out the negative answer, as in our original context it won't make sense. Now we simply use

**w = 2**in our first two equations to get our full answer:

**w = 2**

**l = 2w = 2(2) = 4**

**h = 2l = 2(4) = 8**

**V = lwh = (4)(2)(8) = 64**

**(l+1)(w+1)(h+1) = (5)(3)(9) = 135 = 64+71**

Alex A.

09/28/15

Michael J. answered • 09/14/15

Applying SImple Math to Everyday Life Activities

^{3}.

^{3}+ 71

^{2}+ 6x + 1) = 8x

^{3}+ 71

^{2}+ 6x + 1) + (8x

^{2}+ 6x + 1) = 8x

^{3}+ 71

^{3}+ 14x

^{2}+ 7x + 1 = 8x

^{3}+ 71

^{3}and subtracting 71 on both sides of the equation.

^{2}+ 7x - 70 = 0

^{2}+ x - 10) = 0

^{2}+ x - 10 = 0

^{3}.

^{3}

^{3}. Now we use this volume to check the volume increase.

Alex A.

09/28/15

Alexander B. answered • 09/14/15

PhD in Engineering with 20 yrs of Math and Science Teaching Experience

First, write the system of equation pertinent to the problem definition assuming L, W, H stand for the length, width and height:

H=2L

(W+1)(L+1)(H+1)=LWH+71

Notice that: H=4W and write:

(W+1)(2W+1)(4W+1)=W(2W)(4W)+71

(W+1)(8W

^{2}+2W+4W+1)=8W

^{3}+71

(W+1)(8W

^{2}+6W+1)=8W

^{3}+71

8W

^{3}+6W

^{2}+W+8W

^{2}+6W+1=8W

^{3}+71

Resulting in Quadratic Equation (you can solve it using online Quadratic Equation Solver http://examn8.com/QuadraticEquations.aspx):

14W

^{2}+7W-70=0

which has two solutions but only one positive:

**W=2**(width)

Correspondingly:

**L=4**(length)

**H=8**(height)

Hope this will help.

Alex A.

09/28/15

## Still looking for help? Get the right answer, fast.

Get a free answer to a quick problem.

Most questions answered within 4 hours.

#### OR

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

Jordan K.

09/14/15