Question 220641
Let {{{x}}} = number of cans bought
given:
{{{10/x}}} = price per can in euros
In the other shop, price per can = {{{10/x - .1}}}
The same money is {{{10}}} euros, so
{{{10 = (10/x - .1)*(x + 5)}}}
{{{10 = 10 - .1x + 50/x - .5}}}
{{{.5 = 50/x - .1x}}}
{{{.5x = 50 - .1x^2}}}
{{{5x = 500 - x^2}}}
{{{x^2 + 5x - 500 = 0}}}
by quadratic equation:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = 5}}}
{{{c = -500}}}
{{{x = (-5 +- sqrt( 5^2-4*1*(-500) ))/(2*1) }}}
{{{x = (-5 +- sqrt( 25 + 2000 ))/2 }}}
{{{x = (-5 +- 45)/2 }}}
{{{x = (-5 + 45)/2}}}
{{{x = 20}}} (reject the negative solution)
She bought 20 cans
check answer:
{{{10 = (10/x - .1)*(x + 5)}}}
{{{10 = (10/20 - .1)*(20 + 5)}}}
{{{10 = (.5 - .1)*25}}}
{{{10 = .4*25}}}
{{{10 = 10}}}
OK