Solve the Briefcase Problem: Cost Price of Briefcase

[1/2"]

Homework Statement

A briefcase was sold at a profit of 10%.If the cost price was 5% less and it was sold for $ 7 more , the gain would have been 20% .Find the cost price of briefcase.

2. The attempt at a solution
I assumed cost price to be x
for 10% gain selling price would be 11x/10
& for 20 % gain selling price would be 6x/5 and profit would be x/5
by the condition 3x/20 +7= x/5 =>where x= 140
But the book's answer is $175
I don't know where i am going wrong and also each time the answers are coming different.
Please help me to rectify where i am going wrong .
thank you.

 

[tiny-tim]

A briefcase was sold at a profit of 10%.If the cost price was 5% less and it was sold for $ 7 more , the gain would have been 20% …
…
for 20 % gain selling price would be 6x/5 and profit would be x/5.

Hi 1/2"!

No, it means the gain over the new cost price would be 20%.

(and where did 3/20 come from?)

 

[zgozvrm]

Start with the cost of the briefcase = X dollars
It was sold for S dollars.
Since there was a profit, we know S>X and the amount of the profit was S-X dollars.

The percent of profit is found by dividing the profit by the cost, so

$$\frac{S-X}{X} = 10\% = 0.1$$

Solving for S, you can see that it sold for 1.1X dollars.

Now, if the cost of the briefcase was 5% lower (X-0.05X = 0.95X dolllars)
and, if it sold for $7 more (S+7, or 1.1X + 7 dollars)
then the profit would have been 20%.

So the actual profit would then have been (1.1X + 7) - 0.95X dollars.

Dividing by the cost gives the percent gain:

$$\frac{1.1X + 7 - 0.95X}{0.95X} = 20\% = 0.2$$