Question

A music website charges x dollars for individual songs and y dollars for entire albums. Person A pays $25.92 to download 6 individual songs and 2 albums. Person B pays $33.93 to download 4 individual songs and 3 albums. Write a system of linear equations that represents this situation.

Answer 1

Let $x$ equals to amount charged for downloading individual songs $\Rightarrow$ $y$ equals to amount charged for downloading an entire album.

Solve the system for $y$:
$\left\{{{6x+2y = 25.92,}\atop{4x + 3y = 33.93;}}\right \left\{{{6x+2y = \frac{648}{25},}\atop{4x + 3y = \frac{3393}{100};}}\right \\\left\{{{6x+2y-2y = \frac{648}{25}-2y,}\atop{4x + 3y = \frac{3393}{100};}}\right \left\{{{6x = \frac{648}{25}-2y,}\atop{4x + 3y = \frac{3393}{100};}}\right \\\left\{{{x = \frac{-25y+324}{75},}\atop{4x + 3y = \frac{3393}{100};}}\right \left\{{{x = \frac{-25y+324}{75},}\atop{4\frac{-25y+324}{75} + 3y = \frac{3393}{100};}}\right$
$\left\{{{x = \frac{-25y+324}{75},}\atop{\frac{4(-25y+324)}{75} * 300 + 3y * 300 = \frac{3393}{100} * 300;}}\right \left\{{{x = \frac{-25y+324}{75},}\atop{16(-25y+324)+900y = 10179;}}\right \\\left\{{{x = \frac{-25y+324}{75},}\atop{500y+5184 = 10179;}}\right \left\{{{x = \frac{-25y+324}{75},}\atop{500y = 4995;}}\right \\\left\{{{x = \frac{-25y+324}{75},}\atop{y = \frac{999}{100} = 9.99;}}\right$

Solving the system for $x$ is unoptional since we already have the answer we've been looking for. Your answer is $9.99$.