A necklace, priced between $50 and $100, was on sale at 25% off. When the original price (a whole dollar amount) was discounted, the sale price was also a whole number of dollars. What are the possible original prices for the necklace?
p is a whole number between 50 and 100
(3/4) p whole number
well p = 100 works (then get it for 75)
p = 80 works (then get it for 60)
as a matter of fact anything in there divisible by 4 works
52
56
60
64 etc
I am trying to help my son with the same problem. At first I thought the above answer was correct too. Then I started to second guess myself because $50-$100 is the SALE price so we need to find the ORIGINAL price THEN take 25% off that to get the sale price. The above answer (52, 56, 60, 64....) is if we take 25% off of the sale price ($50-$100). I think we are doing it backwards. ????? I understand that it's every 4 numbers but I think it may be 68, 72, 76.....
If we assume $68 is the original price and take 25% of $68, then we get a sale price of $51. Any thoughts? Again, I have no idea which way is correct.
21
To find the possible original prices for the necklace, we need to consider the discount and the fact that the sale price must be a whole number of dollars.
Let's assume the original price of the necklace is x dollars.
If the necklace is on sale at 25% off, the sale price is 0.75x dollars (since the sale price is 100% - 25% = 75% of the original price).
Given that the sale price must be a whole number of dollars, we can set up the following equation:
0.75x = y, where y is a whole number.
We also know that the sale price is between $50 and $100. So, we have the inequality:
50 ≤ y ≤ 100.
Now, let's substitute the value of y in terms of x into the inequality:
50 ≤ 0.75x ≤ 100.
To solve this inequality, we can divide all parts of the inequality by 0.75:
(50 / 0.75) ≤ (0.75x / 0.75) ≤ (100 / 0.75).
Simplifying, we get:
66.67 ≤ x ≤ 133.33.
Since the original price must be a whole dollar amount, the possible original prices for the necklace are $67, $68, $69, ..., $131, $132, $133.
Therefore, the possible original prices for the necklace are $67 to $133, inclusive.