Three items

The price of a product is determined by these three items: the price of equipment (hardware), the price of software, and the profit. The price of the software was 500 Kč higher than three times the price of the hardware. The profit was set twice as high as the price of the hardware. After the first year, the selling price of the product fell by 1/4 of the original price, and after the second year, the price fell by 20% of the price in the previous year. After these discounts, the product was sold for 7 500 Kč.
Using an equation or system of equations, calculate how many percent of the original price the original profit made up.

Final Answer:

p =  32 %

Step-by-step explanation:

$$\begin{gathered} s=500+3h \\ z=2h \\ {r}_1=1-\frac{1}{4}=\frac{1\cdot 4}{4}-\frac{1}{4}=\frac{4}{4}-\frac{1}{4}=\frac{4-1}{4}=\frac{3}{4}=0.75 \\ {r}_2=100\%-20\%=1-\frac{20}{100}=0.8 \\ r=r_1\cdot r_2=\frac{3}{4}\cdot \frac{4}{5}=\frac{3\cdot 4}{4\cdot 5}=\frac{12}{20}=\frac{3}{5}=0.6 \\ a\cdot r=7500 \\ a=7500/r=7500/\frac{3}{5}=7500:\frac{3}{5}=7500\cdot \frac{5}{3}=\frac{7500\cdot 5}{3}=\frac{37500}{3}=12500\text{Kc} \\ s+h+z=a \\ 500+3h+h+2h=a \\ 500+3h+h+2h=12500 \\ 500+3\cdot h+h+2\cdot h=12500 \\ 6h=12000 \\ h=\frac{12000}{6}=2000 \\ h=2000 \\ z=2\cdot h=2\cdot 2000=4000\text{Kc} \\ p=100\cdot \frac{z}{a}=100\cdot \frac{4000}{12500}=\frac{100\cdot 4000}{12500}=\frac{400000}{12500}=32\% \end{gathered}$$

Try another example