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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 tot

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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?

Jan 23, 2015

#2
+94618
+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....

Jan 23, 2015

#1
+17747
+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%

Jan 23, 2015
#2
+94618
+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