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# Awinemaker is adding certain amounts of wine that contain 18% alcohol and 12% alcohol. he needs to produce 30 gallons of wine with 14% alcohol . how many gallons of each kind of wine does he need? ​

• Réponse publiée par: elaineeee

10 gallons of wine at 18% alcohol

20 gallons of wine at 12% alcohol

Step-by-step explanation:

x   <-- gallons of wine at 18% alcohol

y   <-- gallons of wine at 12% alcohol

z=14

18x + 12y = 30z   <-- eq1

x+y =30     <--  total gallons should equal 30

y=30-x       <-- eq2

18x + 12(30-x) = 30(14)

18x +360 - 12x = 420

18x - 12x = 420 -360

6x = 60

x=60/6

x = 10

y= 30 - 10

y= 20

Extra

x < y       <--  a weaker wine is cheaper , so more gallons of the weaker wine will allow more profit

• Réponse publiée par: Grakname

i hope this helps you

• Réponse publiée par: elaineeee

yes, josh's solution is correct.

step-by-step explanation:

this is josh’s solution for the equation x^2 + 12x + 32 = 0:

x^2 + 12x +32 = 0

x^2 + 12x = -32                   (32 is move to the other side that is why it became negative -32 and that is correct)

x^2 + 12x +36 = -32 + 36       (both sides are added with 36 so that the left side could be a perfect square: the process is completing the square: adding any the same number for both sides will result to the same original equation)

〖(x+6)〗^2 = 4           (the left side is a perfect square so it is right)

x + 6 = ±4                           (square of any value is ± so it is right)

x=-2                                     (get the possible values of x)

x=-10

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Awinemaker is adding certain amounts of wine that contain 18% alcohol and 12% alcohol. he needs to p...