Grade 8 - Algebra #4

Algebra Level 3

A stationery shop sells only one kind of notebook, with the list price at $120\%$ of the production cost, such that the total net profit would be $\$28$ if unchanged. But it didn't sell well, so they decided to take $10\%$ off from the list price of it when there were exactly $100$ notebooks left. The actual total net profit was $\$23.2$ .

Given that the production cost doesn't change at all and the stock doesn't get replenished, how many notebooks did they sell?

Detail: Ignore all of the other factors aside from notebook selling. Examples of things to ignore - employee paycheck, rent of the shop, food expenses, etc.

Image source: ENGLISH@ Fernand Léger, "Notebook: Page n°1"

This problem is a part of <Grade 8 - Algebra> series .

The answer is 350.

1 solution

Boi (보이)
Jul 9, 2017

Let the production cost be $x$ , and the total amount of notebooks they sold be $y$ .

Then the production cost, no matter the changes of the list price, is $xy$ .

And the expected total net profit before the price change was $1.2xy-xy=0.2xy=28$

$xy=140~\cdots~\boxed{A}$ .

	List price	Sold stocks	Gross profit (=Production cost + Net profit)
Before price change	$1.2x$	$y-100$	$1.2x(y-100)$
Price change	$\times0.9$	-	-
After price change	$1.08x$	$100$	$108x$
Overall	-	-	$xy+23.2$

From the table above, we see that $1.2x(y-100)+108x=xy+23.2$ .

$0.2xy-12x=23.2$

$xy-60x=116~\cdots~\boxed{B}$ .

Subtract $\boxed{B}$ from $\boxed{A}$ , and you get $60x=24$ , which leads to $x=0.4$ .

Substituting to $\boxed{A}$ , we get $y=350$ .

Therefore, the stationery shop sold $\boxed{350}$ notebooks.

Grade 8 - Algebra #4

The answer is 350.

1 solution

0 pending reports