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25 Dec 2024, 07:11
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Total weight of coffee = 240000
Number of 8-pound bags and 12-pound bags must each fall between 10,000 and 20,000
Let x be the number of 8 pound bags and y be the number of 12 pound bags
So,
8x + 12y = 240000
=> 2x + 3y = 60000
Also,
10,000≤x≤20,000
10,000≤y≤20,000
Now,
y = (60000-2x)/3
Since y should be an integer the right hand side value should be divisible by 3
So, we substitute values of x and see that 12000 and 18000 satisfy this, but we also observe that for 18000 we get y = 8000 which is not possible since y value should be between 10000 and 20000
y = (60000-2*12000)/3 = 36000/3 = 12000
So x=12000 and y = 12000
Number of 8-pound bags and 12-pound bags must each fall between 10,000 and 20,000
Let x be the number of 8 pound bags and y be the number of 12 pound bags
So,
8x + 12y = 240000
=> 2x + 3y = 60000
Also,
10,000≤x≤20,000
10,000≤y≤20,000
Now,
y = (60000-2x)/3
Since y should be an integer the right hand side value should be divisible by 3
So, we substitute values of x and see that 12000 and 18000 satisfy this, but we also observe that for 18000 we get y = 8000 which is not possible since y value should be between 10000 and 20000
y = (60000-2*12000)/3 = 36000/3 = 12000
So x=12000 and y = 12000
25 Dec 2024, 07:38
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Since 240k pounds must be distributed among the 2 different bags
240000 = 8X + 12Y
10000 < X > 20000
10000 < Y < 20000
I'd simplify in order to ge the following equation
(60000 - 2x)/3 = y
and y must be an integer, so trying values
if x= 10000 then (60000-20000)/3 = not an integer!
if x = 12000 then (60000 - 24000)/3 =12000, which satisfies the question and is an integer
Final solution is 8 pounds and 12 pounds bags 12,000 units each.
240000 = 8X + 12Y
10000 < X > 20000
10000 < Y < 20000
I'd simplify in order to ge the following equation
(60000 - 2x)/3 = y
and y must be an integer, so trying values
if x= 10000 then (60000-20000)/3 = not an integer!
if x = 12000 then (60000 - 24000)/3 =12000, which satisfies the question and is an integer
Final solution is 8 pounds and 12 pounds bags 12,000 units each.
25 Dec 2024, 08:33
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Bookmarks
Let's say there're x 8-pound bags are y 12-pound bags. Then: \(240=8x+12y\)
Dividing the whole equation by 4, we get \(60=2x+3y\)
As both 60 and 3y are divisible by three, then 2x must also divide into 3 => and the only way for this to work is if x itself is divisible into 3.
From the answer options, the only suitable variant is \(x=12k\). Putting it into the equation: \(60=2*12+3y=24+3y\)
So, \(3y=36\) and \(y=12\)
Therefore, the answers are 12,000 for both bag types.
Dividing the whole equation by 4, we get \(60=2x+3y\)
As both 60 and 3y are divisible by three, then 2x must also divide into 3 => and the only way for this to work is if x itself is divisible into 3.
From the answer options, the only suitable variant is \(x=12k\). Putting it into the equation: \(60=2*12+3y=24+3y\)
So, \(3y=36\) and \(y=12\)
Therefore, the answers are 12,000 for both bag types.
