Question 26874: Hello from cold cold Finland
Ok I have the following problem, or actually I have a few problems that are
similar but have little idea about how they should be solved. Anyway the problem
is as follows:
"When the price of a product was reduced by 20%, the sales in euros rose by 4%.
Find the percentage increase in the number of products sold."
Hope that you don't feel insulted if I mention that euros are the currency
used in Finland and most countries in the European Union. Just thought I'd
err on the side of caution and mention this fact.
Ok that's it really. This question is from an old entrance examination paper
for a school that I would like to attend and I would be very grateful for any
assistance that you could give me. I took a look at your other percentage problems and found a few quite interesting.
Thanks again for any instance that you are able to give.
Take care.
t. ryan
Answer by bmauger(101)   (Show Source):
You can put this solution on YOUR website! It's a good problem, gave me pause to think and break out the pencil in paper for a second. It's easier solved if you create fake values (say that originally there's 100 products sold at 100 Euro each then make the changes and see what the product increase must be, then express it as a percentage), but I'll go through it the (slightly) harder way.
First, let's define our variables. Let's say that before the change in price & cost, the merchant was selling "x" amount of product at "y" euros/product. His pre-change income would be x times y euros.
After the change, we are told that his income rose 4%. This means that his new income is now 1.04(xy) (100% + 4%=1.04). We know that he's now selling it at a new rate of .8y (100%-20%=.8). To find the number of product he's now selling, we simply divide the new income by the new rate or:
 In other words, he's sell 1.3 times his original sales, or selling selling 30% more product.
Looking at it in a table might make it a bit more clear:
Old sales: x products times y rate = xy income
New sales: ? products times .8y rate = 1.04xy income
And solving for our question mark we get 1.3x.
|
|
|
