IVAN N. answered • 05/29/25
Certified algebra/calculus/stats tutor with 8 years of experience
This can be evaluated by using a system of equations, with one equation being for the data sizes and the other being for the number of downloads of each version. Let x be defined as the number of downloads of the standard quality version and y be defined as the number of downloads of the high quality version. The system can be set up as follows:
2.7x + 4.9y = 4617 (sizes)
x + y = 1050 (downloads)
We can begin by solving the bottom equation for y. Subtract x from both sides of it. The system now becomes:
2.7x + 4.9y = 4617
y = 1050 - x
We now have an equation in y that we can substitute into the top equation in place of y to solve for x:
2.7x + 4.9(1050 - x) = 4617
Next, distribute the 4.9:
2.7x + 5145 - 4.9x = 4617
Combine like terms:
-2.2x + 5145 = 4617
Subtract 5145 from both sides:
-2.2x = -528
Finally, divide both sides by -2.2:
x = 240
We now know x, which we defined as the number of standard quality version songs downloaded. We can now substitute this number into any above equation. Let’s substitute it into the bottom one from above then solve it for y:
x + y = 1050
240 + y = 1050
Subtract 240 from both sides:
y = 810, which we defined as the number of high quality version songs downloaded.
We will need to check these results by inserting them into both equations to see if they are true:
The original equations were
2.7x + 4.9y = 4617
x + y = 1050
Substitution:
2.7(240) + 4.9(810) = 4617
648 + 3969 = 4617, which is true.
240 + 810 = 1050, which is also true.
Both results gave true statements, so there were 240 standard quality downloads and 810 high quality downloads.
