# the price of an item

• Apr 21st 2013, 11:02 PM
usre123
the price of an item
The price of a certain item was \$10 in 1990 and it has gone up by \$2 per year since 1990. If this trend continues, in what year will the price be \$100?

OA later
• Apr 21st 2013, 11:05 PM
usre123
Re: the price of an item
A large solid cube is assembled by gluing together identical unpainted small cubic blocks. All six faces of the large cube are then painted red. If exactly 27 of the small cubic blocks that make up the large cube have no paint on them, how many small cubic blocks make up the large cube?

OA later
• Apr 21st 2013, 11:05 PM
MarkFL
Re: the price of an item
How long will it take the price to increase by \$90 if it increases \$2 per year?
• Apr 21st 2013, 11:07 PM
usre123
Re: the price of an item
yes.
• Apr 21st 2013, 11:09 PM
usre123
Re: the price of an item
the OA is 2035. my answer is coming out to be 2036 by using the sum of arithmetic formula, where a=10, d=2, and l=100. n comes out to be 46.
• Apr 21st 2013, 11:19 PM
MarkFL
Re: the price of an item
You don't want to use the summation formula if you are going to use the arithmetic progression approach, you want to use the formula for the nth term:

\$\displaystyle a_n=a_1+(n-1)d\$

With \$\displaystyle a_n=100,\,a_1=10,\,d=2\$ we find:

\$\displaystyle 100=10+2(n-1)\$

\$\displaystyle 90=2(n-1)\$

\$\displaystyle n-1=45\$

You see, we want the value of n - 1, not n, as year zero is 1990, not year 1.
• Apr 22nd 2013, 12:21 AM
usre123
Re: the price of an item
Ok, thanks. And any help with the cube one?
• Apr 22nd 2013, 12:33 AM
MarkFL
Re: the price of an item
Quote:

Originally Posted by usre123
Ok, thanks. And any help with the cube one?

What is size of the interior cube with no paint?
• Apr 22nd 2013, 12:35 AM
Prove It
Re: the price of an item
• Apr 22nd 2013, 12:38 AM
MarkFL
Re: the price of an item
Quote:

Originally Posted by Prove It

Yes, this is a very valuable suggestion...follow-up questions are fine within the same topic, but when you tag an unrelated question to an existing topic, it can make a topic convoluted and hard to follow.
• Apr 22nd 2013, 08:16 PM
usre123
Re: the price of an item
ok I'm sorry. Should I move it to a new thread?

I think volume of inner cube is 3, since 3*3*3 = 27. But I dont know where to go from there.
• Apr 22nd 2013, 09:16 PM
MarkFL
Re: the price of an item
Quote:

Originally Posted by usre123
ok I'm sorry. Should I move it to a new thread?

I think volume of inner cube is 3, since 3*3*3 = 27. But I dont know where to go from there.

I think just keeping this in mind for the future is fine.

What must the size of the outer cube be?
• Apr 22nd 2013, 10:05 PM
ibdutt
Re: the price of an item
if 27 cubes have no face painted then have the next bigger cube made be gluing small cubes on each face to complete the cube. Since the bigger cube is made of smaller cubes it should have 64 small cubes. Because 3 cube is 27 and 4 cube is 64. Now you can proceed further