A factory assembles computers and normally produces 600 in x days. i) Write down an expression involving x for the number produced per day

A factory assembles computers and normally produces 600 in x days.
i) Write down an expression involving x for the number produced per day
ii) The rate of production is increased so that 600 are now produced in one day less (x -1). Write down an expression involving x for the number produced
iii) If the difference between these daily rates of production is 50, form an equation in x and show that it reduces to x² - x - 12 = 0
iv) Hence find the number produced per day

Answers

i) the number of computers produced per day is

$\frac{600}{x}$

ii) The new number of computers produced is

$\frac{600}{x - 1}$

iii) If the difference between the two daily rates is 50 then

$\frac{600}{x - 1} - \frac{600}{x}$ = 50

$\frac{600x - 600x + 600}{x^2 - x}$ = 50

600 = 50x² - 50x

50x² - 50x - 600 = 0

It reduces to x² - x - 12 = 0

iv) x² - x - 12 = 0

P = -12; S = -1; N = -4,3

(

$x^2 - 4x$ ) + (3x - 12) = 0

x(x - 4) + 3(x -4) = 0

(x + 3) (x -4) = 0

x - 4 = 0; x = 4

the number of computers produced daily is

$\frac{600}{4}$ = 150 computers

johnmulu answered the question on March 6, 2017 at 08:29

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