Paulo bought and then sold two bikes. He made a 30% profit on the sale of the first bike and a 50% profit of the second bike. If Paulo's total profit was 45%, what was the ratio of his cost for the first bike to his cost for the second bike?

Guest Jan 23, 2015

#2**+5 **

Call the cost of bike 1 = C1 ... and call the cost of bike 2 = C2

And the profit on the sale of bike 1 was 30% more than what he paid for it = 1.3C1 ....and the profit he made on bike 2 was 50% more than what he paid for it = 1.5C2

The amount he received for both bikes [ 1.3C1 + 1.5C2] was 45% above what he paid for both of them ( C1 + C2)...so we have

1.3C1 + 1.5C2 = 1.45(C1 + C2) simplify

1.3C1 + 1.5C2 = 1.45C1 + 1.45C2 rearrange

.05C2 = .15C1 → C1/C2 = .05 / .15 = 1/3....so.. the first bike was 1/3rd the cost of the second bike....

CPhill
Jan 23, 2015

#1**+5 **

Making even divisions: 30% - 35% - 40% - 45% - 50%

From 30% to 45% is three steps; from 50% to 45% is one step.

So, the 50% amount must be 3 times the 30% amount.

Check: let's say that the 30% profit was made on an item that cost $100.00 --> profit = $30.00.

Then the 50$ profit was made on an itme that cost $100.00 x 3 = $300.00 --> profit = $150.00

Total cost ($100.00 + $300.00) = $400.00.

Total profit ($30.00 + $150.00) = $180.00

$180.00 / $400.00 = 0.45 = 45%

geno3141
Jan 23, 2015

#2**+5 **

Best Answer

Call the cost of bike 1 = C1 ... and call the cost of bike 2 = C2

And the profit on the sale of bike 1 was 30% more than what he paid for it = 1.3C1 ....and the profit he made on bike 2 was 50% more than what he paid for it = 1.5C2

The amount he received for both bikes [ 1.3C1 + 1.5C2] was 45% above what he paid for both of them ( C1 + C2)...so we have

1.3C1 + 1.5C2 = 1.45(C1 + C2) simplify

1.3C1 + 1.5C2 = 1.45C1 + 1.45C2 rearrange

.05C2 = .15C1 → C1/C2 = .05 / .15 = 1/3....so.. the first bike was 1/3rd the cost of the second bike....

CPhill
Jan 23, 2015