Question 1190205
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Let's define two brand labels such that
Brand A is worth $90 per bag
Brand B is worth $75 per bag


Let
x = number of bags of brand A
y = number of bags of brand B


The final mix has 50 bags total, so,
x+y = 50
y = 50-x
which we'll use later in substitution



90x = total cost of buying x bags of brand A
75y = total cost of buying y bags of brand B
90x+75y = total cost buying all bags of coffee


We divide this total cost by the number of bags overall (50) to get the final cost per bag ($87)


(total cost)/(total number of bags) = final cost per bag
(90x+75y)/(50) = 87
90x+75y = 87*(50)
90x+75y = 4350


Now we plug in y = 50-x and solve for x.
90x+75y = 4350
90x+75( y ) = 4350
90x+75( 50-x ) = 4350
90x+75*50-75x = 4350
90x+3750-75x = 4350
15x+3750 = 4350
15x = 4350-3750
15x = 600
x = 600/15
<font color=red>x = 40</font>


Then compute the value of y
y = 50-x
y = 50-40
<font color=blue>y = 10</font>


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Answers:
<font color=red>40 bags</font> of the $90 per bag brand.
<font color=blue>10 bags</font> of the $75 per bag brand.
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