Question 937592
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+y=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+0.05y = 0.2*14}}}. 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+0.05y = 0.2*14}}} 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+0.05y = 0.2*14}}} like so...



{{{0.5x+0.05y = 0.2*14}}} Start with the first equation



{{{0.5x+0.05y = 2.8}}} Multiply



{{{0.5x+0.05(14-x) = 2.8}}} Replace {{{y}}} with {{{14-x}}}



{{{0.5x+0.05(14)-0.05x = 2.8}}} Distribute. Now we isolate x



{{{0.5x+0.7-0.05x = 2.8}}}



{{{0.45x+0.7 = 2.8}}}



{{{0.45x = 2.8-0.7}}}



{{{0.45x = 2.1}}}



{{{x = 2.1/0.45}}}



{{{x = 210/45}}}



{{{x = 14/3}}}



{{{x = 4&2/3}}}



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Since {{{x = 4&2/3}}}, this means you need {{{4 & 2/3}}} (4 and two-thirds) oz of apple jack. Use this to find y.



{{{y=14-x}}}



{{{y=14-14/3}}} Plug in {{{x = 14/3}}}



{{{y=42/3-14/3}}}



{{{y=(42-14)/3}}}



{{{y=28/3}}}



{{{y=9&1/3}}}



Because {{{y=9&1/3}}}, you need {{{9&1/3}}} oz of angry orchard.