Suppose is the sale price of an item whose original price is in a 35% off sale. Is directly proportional to ? If it is, enter the constant of proportionality as a decimal, not a percent
If it is 35% off, it is 65% of the original price.
What is the decimal equivalent of 65%?
To determine if is directly proportional to in a 35% off sale, we need to understand what it means for two quantities to be directly proportional.
When two quantities, let's call them and , are directly proportional, it means that as one quantity increases or decreases, the other quantity changes in the same proportion. In other words, their ratio remains constant.
In this case, we want to check if is directly proportional to . is the sale price of an item, while represents the original price of the item.
Let's assume the original price is $100. During a 35% off sale, the sale price would be:
Sale Price = Original Price - (35% * Original Price)
= Original Price - (0.35 * Original Price)
= (1 - 0.35) * Original Price
= 0.65 * Original Price
Now, let's calculate the ratio of the sale price to the original price:
Ratio = Sale Price / Original Price
= (0.65 * Original Price) / Original Price
= 0.65
The ratio of the sale price to the original price is 0.65. This means that it remains constant at 0.65 for any value of the original price.
Therefore, we can conclude that the sale price () is directly proportional to the original price () in a 35% off sale, with the constant of proportionality being 0.65.