Question

A web store offers two versions of a popular song. the size of the standard version is 2.5 megabytes. the size of the high-quality version is 4.6 megabytes. yesterday there were 1230 downloads of the song, for a total download size of 4797 megabytes. how many downloads of the standard version were there?

Answer 1

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Define x and y :
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Let x the number of 2.5M downloads.
Let y the number of 4.6M downloads.

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Construct Equations :
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There was a total of 1230 downloads.
⇒ x + y = 1230

Total downloaded size was 4797M.
⇒2.5x + 4.6y = 4797

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Find x and y :
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x + y = 1230 -------------------- (1)
2.5x + 4.6y = 4797 ------------ (2)

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From equation 1 :
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x + y = 1230
x = 1230 - y // Take away y on both sides

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Sub x = 1230 - y into equation 2 :
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2.5 (1230 - y) + 4.6y = 4797 // Sub x = 1230
3075 - 2.5y + 4.6y = 4797 // Apply distributive property
3075 + 2.1y = 4797 // Combine like terms
2.1y = 1722 // Take away 3075 from both sides
y = 820 // Divide by 2.1 on both sides

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Sub y = 820 into equation 1 to find x :
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x + y = 1230
x + 820 = 1230 // Sub y = 820
x = 410 // Take away 820 from both sides

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Find the number of each type of downloads :
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Number of 2.5M downloads = x = 410
Number of 4.6M downloads = y = 820

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Answer: There were 410 downloads for the standard version.
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