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Noah’s Café sells special blends of coffee mixtures. Noah wants to create a 20-pound mixture with coffee that sells for $9.20 per pound and coffee that sells for $5.50 per pound. How many pounds of each mixture should he blend to create coffee that sells for $6.98 per pound? a 10 pounds of the $5.50-per-pound coffee, 10 pounds of the $9.29-per-pound coffee b 15 pounds of the $5.50-per-pound coffee, 5 pounds of the $9.20-per-pound coffee c 12 pounds of the $5.50-per-pound coffee, 8 pounds of the $9.20-per-pound coffee d 8 pounds of the $5.50-per-pound coffee, 12 pounds of the $9.29-per-pound coffee

Respuesta :

JeanaShupp

Answer: c 12 pounds of the $5.50-per-pound coffee, 8 pounds of the $9.20-per-pound coffee

Step-by-step explanation:

Let x = Number of pound of first king.

y= Number of pound of second kind.

As per given , we have

[tex]x+y=20\Rightarrow\ y= 20-x (i)\\\\\\9.20x +5.50 y= 6.98(20) \\\Rightarrow\ 9.20x +5.50 y=139.6 (ii)[/tex]

substitute value of y from (i) in (ii), we get

[tex]9.20x +5.50(20-x) =139.6\\\\\Rightarrow\ 9.20x +5.50(20)-5.50x =139.6\\\\\Rightarrow\ 9.20x-5.50x +110 =139.6\\\\\Rightarrow\ 3.7x =139.6-110\\\\\Rightarrow\ 3.7x =29.6\\\\\Rightarrow\ x=\dfrac{29.6}{3.7}=\dfrac{296}{37}\\\\\Rightarrow\ x=8[/tex]

Put this in (i), we get y= 20-8 = 12

Hence,  he should blend 12 pounds of the $5.50-per-pound coffee, 8 pounds of the $9.20-per-pound coffee.

So the correct option is c.