SOLUTION: I'm trying to make a mixed drink, called a johnny jump up. Its 15 oz . 14 oz of 20% alcohol cider... and 1 oz of Jameson. But the issue is I don't have a 20% cider. I have a

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: I'm trying to make a mixed drink, called a johnny jump up. Its 15 oz . 14 oz of 20% alcohol cider... and 1 oz of Jameson. But the issue is I don't have a 20% cider. I have a       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 937592: I'm trying to make a mixed drink, called a johnny jump up. Its 15 oz . 14 oz of 20% alcohol cider... and 1 oz of Jameson.
But the issue is I don't have a 20% cider. I have a 50% alcohol apple jack and 5% alcohol angry orchard. What is the formula to mix these two liquors to come up with a solution that is roughly 20% in alcohol in mixture?
Thank you from a amateur mixologist who is racking his brain to try and figure out the math he forgot in school.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x = amount of alcohol apple jack (in ounces)
y = amount of alcohol angry orchard (in ounces)


You want 14 oz of alcohol cider, so x%2By=14 (since you mix those two to get 14 oz)


Solve for y to get y=14-x


"I have a 50% alcohol apple jack and 5% alcohol angry orchard", so this means we have this equation 0.5x%2B0.05y+=+0.2%2A14. We have 0.5x oz of pure alcohol from the apple jack and 0.05y oz of pure alcohol from the angry orchard. These two amounts of pure alcohol will combine to be equal to 0.2*14 because you'll have 0.2*14 oz of pure alcohol (you want 20% of pure alcohol in the final mix)


We will use the equations 0.5x%2B0.05y+=+0.2%2A14 and y=14-x to find x & y. First we need to find x. So let's plug in y=14-x into 0.5x%2B0.05y+=+0.2%2A14 like so...


0.5x%2B0.05y+=+0.2%2A14 Start with the first equation


0.5x%2B0.05y+=+2.8 Multiply


0.5x%2B0.05%2814-x%29+=+2.8 Replace y with 14-x


0.5x%2B0.05%2814%29-0.05x+=+2.8 Distribute. Now we isolate x


0.5x%2B0.7-0.05x+=+2.8


0.45x%2B0.7+=+2.8


0.45x+=+2.8-0.7


0.45x+=+2.1


x+=+2.1%2F0.45


x+=+210%2F45


x+=+14%2F3


x+=+4%262%2F3


---------------------------------------------------------------------------------------------------------------


Since x+=+4%262%2F3, this means you need 4+%26+2%2F3 (4 and two-thirds) oz of apple jack. Use this to find y.


y=14-x


y=14-14%2F3 Plug in x+=+14%2F3


y=42%2F3-14%2F3


y=%2842-14%29%2F3


y=28%2F3


y=9%261%2F3


Because y=9%261%2F3, you need 9%261%2F3 oz of angry orchard.