Member: Rom

Quote:
Emily and Sarah had a total of $80. After Sarah spent 1/3 of her money and Emily spent $17, Emily had twice as much money as Sarah. How much more money did Emily have than Sarah at first?

asking to solve this w/o algebra is like asking to make an omelet w/o eggs.

This is an algebra problem.

RomFeb 18, 2014

+6251

Quote:
-(8/343)^-(4/3)

Not quite. You forgot the 4th power.

-(8/343) ^(-4/3) =

-(343/8) ^(4/3) =

-((343/8) ^1/3) ⁴ =

-(7/2) ⁴ = -2401/16

RomFeb 18, 2014

+6251

Quote:
What is -10.6666666666666667 in a fraction?

what you're really interested in is what does 0.6666666666666666666 etc. convert to

the trick to this (and it is a trick) is to consider the difference between itself and 10 times itself i.e.

6.666666666666666... - 0.6666666666666666... = 6

so let x = 0.666666666666666666...

10x - x = 6

9x = 6

x = 6/9 = 2/3

suppose you had 0.12121212121212.......

you can consider the difference of 100 times itself and itself

you get

99x = 12

x = 12/99 = 4/33

similarly with repeating patterns of length K, just consider the difference of 10 ^K times itself and itself.

RomFeb 18, 2014

+6251

Quote:
HOW MANY .745" SQUARES CAN BE CUT FROM 16"X14.25" SHEET

this could in general be a very difficult question as you can come up with patterns of squares to cover the sheet in more efficient ways than just the obvious one.

The theoretical maximum is going to be the area of the big sheet divided by the area of a little square which is

16 * 14.25 / (0.745) ² =

16 * 14.25 / (0.745)^2

i.e. 410 squares but you might not be able to find a pattern of squares that matches this

if you just use the obvious pattern and do as well as you can you get

(16/0.745) * (14.25/0.745)

and you see that just using the obvious pattern in this case gets you as many squares as you can theoretically get.

So you can get 410 squares.

RomFeb 18, 2014

+6251

Quote:
The sum of -4 and 8 times a number is multiplied by 3. The result is 15 less than 25 times the number. What is the number?

Let the number be x

the first sentence results in 3(-4 + 8x)

the second sentence is (25x - 15)

and these two are equal

3(-4 + 8x) = 25x - 15

-12 + 24x = 25x - 15 ; add 15-24x to both sides

3 = x

RomFeb 18, 2014

+6251

Quote:
calculate the simple interest on $4500 at 7.3% for 260 days (use the exact method).

I don't know what the "exact method" is but assuming 7.3 annual interest with no compounding you get

I = 4500 * (0.073) * (260/365) =

4500 * 0.073 * (260/365)

RomFeb 17, 2014

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