SOLUTION: Sammy spends 10 Euros on some cans of drink. In another shop she sees that the same cans are each 10 cents cheaper, and she calculates that she could have brought 5 more cans for t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Sammy spends 10 Euros on some cans of drink. In another shop she sees that the same cans are each 10 cents cheaper, and she calculates that she could have brought 5 more cans for t      Log On


   

Question 220641: Sammy spends 10 Euros on some cans of drink. In another shop she sees that the same cans are each 10 cents cheaper, and she calculates that she could have brought 5 more cans for the same money. How many cans did she buy?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = number of cans bought
given:
10%2Fx = price per can in euros
In the other shop, price per can = 10%2Fx+-+.1
The same money is 10 euros, so
10+=+%2810%2Fx+-+.1%29%2A%28x+%2B+5%29
10+=+10+-+.1x+%2B+50%2Fx+-+.5
.5+=+50%2Fx+-+.1x
.5x+=+50+-+.1x%5E2
5x+=+500+-+x%5E2
x%5E2+%2B+5x+-+500+=+0
by quadratic equation:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+5
c+=+-500
x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A%28-500%29+%29%29%2F%282%2A1%29+
x+=+%28-5+%2B-+sqrt%28+25+%2B+2000+%29%29%2F2+
x+=+%28-5+%2B-+45%29%2F2+
x+=+%28-5+%2B+45%29%2F2
x+=+20 (reject the negative solution)
She bought 20 cans
check answer:
10+=+%2810%2Fx+-+.1%29%2A%28x+%2B+5%29
10+=+%2810%2F20+-+.1%29%2A%2820+%2B+5%29
10+=+%28.5+-+.1%29%2A25
10+=+.4%2A25
10+=+10
OK