These answers don't make sense to me...?

Question

You want to build a box to hold your CDs. You want the measurements for the box to be 10 inches long, 6 inches wide, and 5 inches tall. Using the measurements of the box, draw a diagram that illustrates the box. Use it to find the smallest sheet of wood that will be needed to build the box.


I don't know if i'm just being stupid, but I drew the box and found that the smallest piece of wood used was 5x6 in. This would be 30 sq. in. But then it occurred to me that the question might be asking for a sheet of wood you can cut up to make all of the parts. It turns out the answer is 320 sq. in., but I have no idea how to reach that answer. I must be having a major mind lapse... there are more problems; I'll add them.

A designer works on an hourly wage plus markup on materials. If the designer spends 30 hours on a project at $25 an hour and recommends materials costing $4500 with a markup of 30%, what is the designer's fee?

I did 4500 x .3, subtracted that from 4500, added it to 30 x 25. [3150(30 x 25)]. I got $3900, but the correct answer is $2100. I think this is just one huge brain lapse, seriously, but if someone could work me through this problem I'd appreciate it.

One more: Solve: 3m-2(m-3) = 1. The answer is -5. I'm doing something wrong with the order of operations (PEMDAS), I think. Thanks for helping.

I understand the third problem now that I have a variable to substitute for m, but I want to know how to work through it. Thanks!

Answer 1

You need the answer for the sheet of wood you can cut up to make all the parts.

If the box is 10 x 6 x 5 inches^3,

The back of the box is 10" long x 5" tall,
each end of the box is 6" deep x 5" tall (so there are 2 that size)
and the top/bottom of the box are 10" long x 6" deep

Back 10" x 5"
Ends 10" x 6" (together)
Top 10" x 6"
Bottom 10" x 6"

The sheet of wood to make this would be 10" x 23" = 230 sq in

Answer 2

Simple.
totla surface area of wood =
2(lb + bh + hl)
=
2(30 + 50 + 60)
=2 * 140
=280 sq inchs.

2nd one
so total markup for work
is
25 * 30
=750 dollars and for the materials =
30/100*4500
=450*3=1350
Therefore
1350 + 750 = 2100 dollars.

3rd one
3m -2(m-3)
=
3m -2m + 6 = 1
=m = 1-6
=m = -5.
Thus Done

Answer 3

well the last one the 3m-2(m-3)=1
first you must disribute the (-2)
3m+(-2)m+(-2)(-3)=1
which equals 3m-2m+6=1
which simplifies down to m+6=1
subtract the 6 and you get -5

I think you just forgot about the two being negative

I will have to think about the others later

Answer 4

Answer to second question:

30 hrs X $25 per hour = $750

30% of $4,500 = .3 x 4500= $1,350. (The $4,500 is the material price BEFORE the markup.

$750+$1,350 = $2,100

Answer 5

the last question you have to solve like this:

Solve: 3m-2(m-3) = 1.

3x m - 2 x m + 6 = 1
because -2 x -3 equals 6

so m must be -5

Answer 6

For question: 3m-2(m-3)=1
Do () first: 3m-2m+6=1
Next: 1m+6=1
Then: -6 from both sides
Left with: 1m= -5
So: m= -5