Thread: Algebra Question Year 10 problem

Can someone help me with the last part of this problem:

A company makes calculation and has found that the cost C$ of producing X calculators is given by the rule:

C=x(x-2) C is the cost in dollars and x is the number of calculators

It has also fund tha the revenue $R from the sale of the calculators is given by the rule:

R= (x(x+3)

Using the fact that profit equals Revenue minus Cost show that the profit $P from the sale of x cakculators is given by the rule:
P=5x

I have done this bit and can prove that the answer to x(x+3) - x(x-2) is 5x

However I cant get the next bit - please help

The company engineer invents a new production process that shows some improvement and the new rule for producing x calcuators is given by:

C=(x+20) (x-21) What would be the new rule for the profit $P using this new process. So I need to know how to work out

x(x+3) - (x+20) (x-21) I think the last part has something to do with the difference of two squares rule. please show working. Thanks a million

Originally Posted by chreen15

[snip]I need to know how to work out

x(x+3) - (x+20) (x-21) I think the last part has something to do with the difference of two squares rule. please show working. Thanks a million

Expand and simplify:

x(x + 3) = x^2 + 3x.

(x + 20)(x - 21) = x^2 - 21x + 20x - 420 = x^2 - x - 420.

So x(x + 3) - (x + 20) (x - 21) = x^2 + 3x - (x^2 - x - 420) = x^2 + 3x - x^2 + x + 420 = .......

Thanks