SOLUTION: 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

Algebra ->  Equations -> SOLUTION: 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      Log On


   

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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Fv = his cost for each vase
and
1344%2Fv + 80 = selling price of each vase
:
No overall gain, therefore
(v-5)*(1344%2Fv+80) = 1344
(1344%2Fv+80) = 1344%2F%28%28v-5%29%29
%28%281344%2B80v%29%29%2Fv = 1344%2F%28%28v-5%29%29
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