How would you write this out algebraically

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coolgirl26: Senior | Next Rank: 100 Posts; Posts: 71; Joined: Tue Mar 03, 2009 1:24 pm

by coolgirl26 » Sat Apr 18, 2009 5:07 pm

The price of a product is $x . Karen bought R products and then sold 50% of them for Y dollars.

What represents the total amount karen made if her profit was
2 times the cost of the r product

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Source: Beat The GMAT — Problem Solving | Sat Apr 18, 2009 5:07 pm

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Sat Apr 18, 2009 5:27 pm

Since the price of each product is x dollars, R products would've costed Karen x*R dollars. Since she sold 50% of these R products for y dollars, she would've made R/2*y=Ry/2 dollars. Now these Ry/2 dollars subtracted to the total cost of the R products would represent the profit that Karen made and we know that this profit would be 2*x*R since it's 2 times the cost of the R products. With this said, our algebraic expression would be:

Ry/2-xR=2xR.

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m&m: Master | Next Rank: 500 Posts; Posts: 134; Joined: Sun Feb 15, 2009 7:44 pm; Thanked: 14 times

by m&m » Sat Apr 18, 2009 9:03 pm

she first bought R products at x$/prod = Rx
She then sold half her products at y$/prod = 1/2Ry

we know that she profited (sell-cost) 2x the price she originally paid, which is x per product. so if she buys at 10 she sold at 30 (profit is 2x buy price) so
y-x = 2x, or y=3x

so total is -Rx + 1/2R*3x
= 1/2Rx

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