SOLUTION: .} 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 a

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: .} 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 a      Log On

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Question 197937: .} 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?
Found 2 solutions by josmiceli, yellow:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let w= the number of watermelons bought
given:
w+-+30= the number of watermelons sold
1.5%2A%28w+-+30%29= profit made on watermelons sold
200%2Fw= price paid per watermelon bought
--------------------------------------
%28200%2Fw+%2B+1.5%29%2A%28w+-+30%29+=+200
This is (cost/wm + profit/wm)*(actual wm's sold) = investment
200%2Fw+%2B+1.5+=+200%2F%28w+-+30%29
Multiply both sides by w%2A%28w+-+30%29
200%2A%28w+-+30%29+%2B+1.5w%2A%28w+-+30%29+=+200w
200w+-+6000+%2B+1.5w%5E2+-+45w+=+200w
1.5w%5E2+-+45w+-+6000+=+0
w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1.5
b+=+-45
c+=+-6000
w+=+%28-%28-45%29+%2B-+sqrt%28+%28-45%29%5E2-4%2A1.5%2A%28-6000%29+%29%29%2F%282%2A1.5%29+
w+=+%2845+%2B-+sqrt%28+2025+%2B+36000+%29%29%2F3+
w+=+%2845+%2B-+sqrt%28+38025+%29%29%2F3+
w+=+%2845+%2B-+195%29%2F3+
w+=+240%2F3 (ignore negative result)
w+=+80
She bought 80 watermelons originally
check answer:
200%2F80+=+2.5= price paid per watermelon
80+-+30+=+50= watermelons sold
2.5%2A50+=+125= price paid for water melons sold
1.5%2A50+=+75= profit on watermelons sold
125+%2B+75+=+200
OK

Answer by yellow(1) About Me  (Show Source):
You can put this solution on YOUR website!
A compound interest table shows the compounded amount per dollar of principal. True or False.