SOLUTION: 92. Recovering an investment. The manager at Cream of the Crop bought a load of watermelons for $200. She priced the melons so that she would make $1.50 profit on each melon. Wh

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: 92. Recovering an investment. The manager at Cream of the Crop bought a load of watermelons for $200. She priced the melons so that she would make $1.50 profit on each melon. Wh      Log On

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Question 191945This question is from textbook Elementary and Intermediate Algebra
: 92. Recovering an investment. The manager at Cream of
the Crop bought a load of watermelons for $200. She
priced the melons so that she would make $1.50 profit on
each melon. When all but 30 had been sold, the manager
had recovered her initial investment. How many did she
buy originally?
This question is from textbook Elementary and Intermediate Algebra

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!

Let x= the number of melons bought originally
Given:
200%2Fx= Original cost per melon
200%2Fx+%2B+1.5= Selling price per melon
x+-+30= number of melons sold
--------------
200+=+%28200%2Fx+%2B+1.5%29%2A%28x+-+30%29
200+=+200+-+6000%2Fx+-+45+%2B+1.5x
6000%2Fx+-+1.5x+%2B+45+=+0
6000+-+1.5x%5E2+%2B+45x+=+0
-1.5x%5E2+%2B+45x+%2B+6000+=+0
-15x%5E2+%2B+450x+%2B+60000+=+0
-x%5E2+%2B+30x+%2B+4000+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+-1
b+=+30
c+=+4000
x+=+%28+30+%2B-+sqrt%28++30%5E2+-+4%2A%28-1%29%2A4000+%29%29%2F%282%2A1%29+
x+=+%2830+%2B-+sqrt%28+900+%2B+16000+%29%29%2F+2+
x+=+%2830+%2B-+sqrt%28+16900+%29%29%2F+2+
x+=+%2830+%2B-+130%29%2F2
x+=+160%2F2
x+=+80
She bought 80 melons originally
check answer:
200+=+%28200%2Fx+%2B+1.5%29%2A%28x+-+30%29
200+=+%28200%2F80+%2B+1.5%29%2A%2880+-+30%29
200+=+%282.5+%2B+1.5%29%2A%2850%29
200+=+4%2A50
200+=+200
OK