Question

Español A Web music store offers two versions of a popular song. The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.1 MB. Yesterday, there were 880 downloads of the song, for a total download size of 3153 MB. How many downloads of the high-quality version were there? Number of high-quality version downloads:

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the representation of the two versions

Let x represent the number of standard versions

Let y represent the number of high-quality versions

STEP 2: Interpret the statements using mathematical notations

$\begin{gathered} one\text{ standard version}=2.8 \\ one\text{ high-quality version}=4.1 \\ x+y=880-----equation\text{ 1} \\ 2.8x+4.1y=3153----equation\text{ 2} \end{gathered}$

STEP 3: Solve the equations simultaneously

Make x the subject of the equation 1

$x=880-y--------equation\text{ 3}$

STEP 4: Substitute for x in equation 2 and solve for y

$\begin{gathered} 2.8(880-y)+4.1y=3153 \\ 2464-2.8y+4.1y=3153 \\ 1.3y=3153-2464=689 \\ Divide\text{ both sides by 1.3} \\ \frac{1.3y}{1.3}=\frac{689}{1.3} \\ y=530 \end{gathered}$

Since it is stated in step 1 that y is the number of high-quality version download, therefore the number of high-quality version downloads is 530