Expert: Josh - 2/9/2006

Question
A man sold two bikes for $3400 each. On one he made a profit of5% and on the other he made a loss of 8%. Find the total cost price.

My answer is not correct even though I followed the procedure in the text. My answer was off by a few dollars. Could you please outline the problems by steps. Thanks.

Answer
Hi Larry,

Let us assign a variable for each unknown quantity. We can use "x" and "y" to denote the sales price of the first and second bike, respectively. Similarly, let "X" and "Y" denote the original price of these two bikes.

We were told that each bike is sold for $3400. Thus, x=3400 and y=3400.

How are "X" and "Y" (the original cost) related to "x" and "y" (the sales price)?

Well, we earned a 5% profit on the first bike. Since the "sales price"="original price"+"profit"
x=X+0.05*X=1.05*X ...[#2]
Interpretation: First bike actually costs less than $3400.
Reason: Since X < x

For the second bike, we made a loss of 8% (loss is regarded as negative gain, so we treat this as -0.08), so, y=Y+(-0.08*Y)=0.92Y ...[#3]
Interpretation: Second bike actually costs more than $3400.
Why? Because Y > y

From [#2], the original cost for bike 1 is X=x/1.05.
From [#3], the original cost for bike 2 is Y=y/0.92.

So, the total cost is
X+Y = (x/1.05)+(y/0.92)
   = x*[(1/1.05)+(1/0.92)] since x=y
   = 3400*[(1/1.05)+(1/0.92)]
The combined cost of the bikes, X+Y = $6933.75.

Cheers.