Question 1030109
 John bought some vases for $1344.
 5 of them were broken during delivery.
 He then sold the rest of the vases each at $80 more than its original cost.
 He made no overall gain or loss.
 Find the number of vases John bought.
:
let v = no. of vases he bought
then, since 5 were broken;
(v-5) = no. of vases he sold 
:
{{{1344/v}}} = his cost for each vase
and
{{{1344/v}}} + 80 = selling price of each vase
:
No overall gain, therefore
(v-5)*({{{1344/v}}}+80) = 1344
({{{1344/v}}}+80) = {{{1344/((v-5))}}}
{{{((1344+80v))/v}}} = {{{1344/((v-5))}}}
cross multiply
1344v = (1344+80v)(v-5)
FOIL the right side
1344v = 1344v - 6720 + 80v^2 - 400v
Subtract 1344v from both sides, form a quadratic equation
0 = 80v^2 - 400v - 6720
Simplify, divide equation by 80
v^2 - 5v - 84 = 0
Factors to
(v-12)(v+7) = 0
The positive solution
v = 12 vases purchased originally
:
:
See if that works out
1344/12 = $112 each
7(112+80) = $1344, total return on 7 vases sold