A shopkeeper sells a hat for $14.the amount he gains is three times the amount he loses when he tries to sell it for $8.find the cost price? A.9 B.8.5 C.9.5 D.11 E.10
10
Can you show the formula
Let's assume the cost price of the hat is "x" dollars.
When the shopkeeper sells the hat for $14, he gains 3 times the amount he loses when he tries to sell it for $8.
Let's calculate the amount he loses when he sells the hat for $8:
Amount lost = Cost Price - Selling Price
Amount lost = x - 8
Now, according to the given information, when the shopkeeper sells the hat for $14, he gains three times the amount lost:
Amount gained = 3 * Amount lost
Amount gained = 3 * (x - 8)
Given that the amount gained when he sells the hat for $14 is $14, we can set up the equation:
14 = 3(x - 8)
Simplifying the equation:
14 = 3x - 24
3x = 14 + 24
3x = 38
x = 38/3
x ≈ 12.67
The cost price of the hat is approximately $12.67.
Since none of the answer choices match exactly, we can round the cost price to the nearest option:
A. 9
B. 8.5
C. 9.5
D. 11
E. 10
Rounding 12.67 to the nearest option gives us:
D. 11
Therefore, the closest option for the cost price would be D. 11.
To find the cost price of the hat, we can set up a mathematical equation based on the given information.
Let's denote the cost price of the hat as "x".
According to the given information, the shopkeeper sells the hat for $14, so he gains 3 times the amount he loses when selling it for $8.
When selling for $8 he loses (14 - 8) = $6.
Therefore, the gain is 3 times the loss, which means the gain is 3 * $6 = $18.
We can now set up the equation: x + $18 = $14.
To get the cost price "x" alone on one side of the equation, we can subtract $18 from both sides: x = $14 - $18 = -$4.
Negative cost price doesn't make sense in this context, so there must be a mistake in the given options or the problem itself.
Based on the given options, none of them would be correct. Please double-check the question or the available answer choices.