A software company sells an education version and a commercial version of its popular image editing software. Let x be the number of education version copies sold and y be the number of commercial version copies sold.
1. During the month of January 500 copies of the software are sold, then
x+y=500.
2. If the price of the education version is $150, then x educational version copies cost $150x. If the price of the commercial version is $600, then y commercial version copies cost $600y. The total sales are $(150x+600y) that is $180,000, then
150x+600y=180,000.
3. The system that of equations matches the situation is
[tex]\left\{\begin{array}{l}x+y=500\\150x+600y=180,000\end{array}\right..[/tex]
Solve this system. First, express x from the first equation:
x=500-y.
Substitute this x into the second equation:
150(500-y)+600y=180,000,
75,000-150y+600y=180,000,
450y=105,000,
[tex]y=\dfrac{105,000}{450}=\dfrac{700}{3}.[/tex]
Then
[tex]x=500-\dfrac{700}{3}=\dfrac{800}{3}.[/tex]
Answer: they sold nearly 267 educational version copies and nearly 233 commercial version copies
