MHB Word Problem: Songs Downloaded

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To solve the problem of determining how many high-quality songs were downloaded, a system of equations is suggested. The first equation is based on the total size of the downloads: 2.3S + 4.2H = 4077, where S represents standard versions and H represents high-quality versions. A second equation is needed, which can be derived from the total number of downloads: S + H = 1120. By solving these two equations simultaneously, the number of high-quality songs downloaded can be calculated. This approach provides a structured method to tackle the word problem effectively.
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My homework question is "the standard version of a song is 2.3mb and high quality is 4.2mb. There was 1120 downloads for a total of 4077mb. How many high quality songs were downloaded?" I'm having an issue creating the formula needed to solve this word problem!
 
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reader1018 said:
My homework question is "the standard version of a song is 2.3mb and high quality is 4.2mb. There was 1120 downloads for a total of 4077mb. How many high quality songs were downloaded?" I'm having an issue creating the formula needed to solve this word problem!

Hi reader1018,

I think we can set up a system of equations to solve this. Let's call $S$ the number of standard versions downloaded and $H$ the number of high quality versions downloaded. We are told that $2.3S+4.2H=4077$. We need a second equation though to solve for both variables. What else do we know?
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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