There are 60 Country CDs and 136 Rock CDs.
Rock and country CDs = 196
Country CD = x
Rock CD = x + 76
Country CD + Rock CD = 196
x + (x + 76) = 196
2x = 196 - 76
2x = 120
2x / 2 = 120 / 2
x = 60 * number of Country CD
Rock CD = x + 76 = 60 + 76 = 136
To check:
Country + Rock = 196
60 + 136 = 196
196 = 196
let's firstly convert the mixed fractions to improper fractions, and then use the LCD, which in this case is 4, to sum them up.
![\bf \stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}}~\hfill \stackrel{mixed}{4\frac{3}{4}}\implies \cfrac{4\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{19}{4}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{13}{4}+\cfrac{19}{4}\implies \stackrel{\textit{using the LCD of 4}}{\cfrac{13+19}{4}}\implies \cfrac{32}{4}\implies 8](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%204%2B1%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B13%7D%7B4%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B4%5Cfrac%7B3%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B4%5Ccdot%204%2B3%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B19%7D%7B4%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Ccfrac%7B13%7D%7B4%7D%2B%5Ccfrac%7B19%7D%7B4%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20LCD%20of%204%7D%7D%7B%5Ccfrac%7B13%2B19%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B32%7D%7B4%7D%5Cimplies%208)
Solution to equation
for all real values of x is
.
<u>Step-by-step explanation:</u>
Here we have ,
. Let's solve :
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⇒ 
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⇒ 
⇒ 
⇒ 
By quadratic formula :
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⇒ 
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But at
we have equation undefined as
. Hence only solution is :
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Since , 
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Now , General Solution is given by :
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Therefore , Solution to equation
for all real values of x is
.