A man buys 3 items for $100. Each item is 50% less than the first. Total of all 3 has to be $100. Is this possible?
57.25
28.63
14.31
It is possible if we neglect the rounding of the cents.
Ratio of prices is 1:2:4, and 1+2+4=7
So the prices are:
$100*(1/7), $100*(2/7), $100*(4/7), or
$14.29
$28.57
$57.14
Note that $14.29 has been rounded up half a cent, so $14.29>($28.57/2)
To check if it is possible for a man to buy three items for $100, each item being 50% less than the first, we can break it down step by step.
Let's assume the price of the first item is X dollars. According to the given information, the second item would be priced at 50% less than the first item, which means the second item would be priced at (X - 0.5X) = 0.5X dollars.
Similarly, the third item would be priced at 50% less than the second item, which would be (0.5X - 0.5(0.5X)) = 0.25X dollars.
Now, we know that the total cost of the three items is $100. So, we can sum up the prices of the three items:
X + 0.5X + 0.25X = 100
Combining like terms, we get:
1.75X = 100
To solve for X, we divide both sides of the equation by 1.75:
X = 100 / 1.75 = 57.14 (rounded to two decimal places)
Therefore, the initial price of the first item should be $57.14 to meet the condition of the problem.
Now, let's calculate the prices of the second and third items based on the given information:
Second item price = 0.5 * 57.14 = $28.57 (rounded to two decimal places)
Third item price = 0.25 * 57.14 = $14.29 (rounded to two decimal places)
Let's check if the total cost of the three items adds up to $100:
57.14 + 28.57 + 14.29 = $100
So, it is indeed possible for a man to buy three items for $100, with each subsequent item being 50% less than the previous item.