Quadratic Equation - Number

[Guest]

A money safe contains a number of drawers. Each drawer has as many dividers as there are drawers. In each divider there are 4 times as many dollars as there are drawers.

Total sum of money in safe - $5,324

Determine number of drawers.

Let x = number of drawers.

Let d = number of dividers.

Let m = number of dollars.

Let s = sum.

x = d

4m = x

s = 5,324

I don't know how to proceed from here.

[Guest]

Let x = number of drawers.
Let d = number of dividers per drawer.
Let m = number of dollars per divider.
Let s = total number of dollars.

d = x because "Each drawer has as many dividers as there are drawers"
m = 4x because "In each divider there are 4 times as many dollars as there are drawers."
s = 5324 because "Total sum of money in safe - $5,324"

Another way of calculating s is to realise that
s = mdx
because "total number of dollars" = "dollars per divider" times "dividers per drawer" times "number of drawers"

Putting these equations together we get
s = mdx
5324 = mdx
5324 = (4x)dx
5324 = (4x)(x)x = 4x^3
Divide both sides by 4 to get
1331 = x^3
Cube root to get
11 = x = number of drawers.

Hope this helped,

R. Baber.

[Guest]

Keep it simple......

Let d = number of drawers
Then d^2 = number of dividers.....we are told each drawer has same number of dividers as there are drawers.
Then 4d = number of dollars in each divider.....we are told dollars in each divider is 4 times number of drawers
That gives 4d^3 = 5324 dollars total in the safe
Which simplifies to.... d^3 = 1331 ...so...d = 11 drawers in the safe.

.......simple......

[Guest]

How is the cube root calculated ?

[Guest]

Normally nowadays using a calculator.

[Guest]

Then d^2 = number of dividers.....we are told each drawer has same number of dividers as there are drawers."

One question:

Is the drawer number squared because the dividers are included ?

[Guest]

There are "d" drawers with "d" dividers in each drawer so that is "d" x "d" OR d^2

If there had been 10 drawers and 10 dividers in each drawer then there would have been 10 x 10 dividers = 100 dividers = 10^2 dividers

[Guest]

I understand it now. Thanks.