Algebra verbal find the amount of sold items Hey I am having an exam tomorrow, so I looked up at some verbal algebra questions, and found one that I could not solve, because I don't really understand how would I do this.
The question is like this:
An IKEA agent bought beds for 60,000 dollars. 1/4 of the beds that he bought, he sold them with a 80% profit. 4 beds were sold without any profit and rest of the beds were sold with a lose of 10% per bed. Overall he made a profit of 9500 dollars.
How many beds did the agent buy?
How much did the agent pay per bed?
I totally don't understand how would I solve this question, could someone give me a tip? the 1/4 part confuses me
 A: Let $B$ be the number of beds. Let $P$ be the price he paid per bed.
$$60000=BP$$
$$\begin{align}9500&=\frac{B}4\cdot0.8\cdot P + \left(\frac{3B}{4}-4\right)\cdot(-0.1)\cdot P\\
&=\frac{BP}{4}\left(0.8+3\cdot(-0.1)\right)-4\cdot(-0.1)\cdot P\end{align}$$
A: Here's my informal solution for this.
We want to know how 60000 is calculated. This is given by the following formula (quantity times price):
$$60000 = q \cdot p$$
Let's call $q_1$ the quantity of beds sold with profit and $q_2$ the quantity beds sold with loss. Then we can say:
$$q = q_1 + q_2 + 4$$
Because 25% of the beds was sold with profit, we know that:
$$q_1 \cdot p = 15000$$
We know that the loss on the beds that made a loss is 2500, because the profit on the profiting beds is $15000 \cdot 0.8$ and the total profit is given as 9500.
From this we can formulate the formula for $q_2$:
$${q_2 \cdot p \over 10} = 2500 $$
Or:
$${q_2 \cdot p} = 25000 $$
Now we can put all this into the original formula, and we get this:
$$60000 =  ({25000 \over p} + {15000 \over p} + 4)  \cdot p$$
$$60000 =  25000 + 15000 + 4 \cdot p$$
$$p = 5000$$
$$q = 12$$
