SOLUTION: 16 lbs of Brand M Cinnamon costing $17/lb. was made by combining Indonesian cinnamon
which costs $19/lbs with Thai cinnamon which costs $11/lb. Find out how much of each type
o
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-> SOLUTION: 16 lbs of Brand M Cinnamon costing $17/lb. was made by combining Indonesian cinnamon
which costs $19/lbs with Thai cinnamon which costs $11/lb. Find out how much of each type
o
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Question 1186116: 16 lbs of Brand M Cinnamon costing $17/lb. was made by combining Indonesian cinnamon
which costs $19/lbs with Thai cinnamon which costs $11/lb. Find out how much of each type
of cinnamon was used to make the Brand M blend. Found 2 solutions by Theo, greenestamps:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! let x = number of pounds of indonesian cinnamon.
let y = number of pounds of thai cinnamon.
let x + y = number of pounds of brand M cinnamon.
your equations are:
x + y = 16
19 * x + 11 * y = 17 * (x + y)
simplify the second equation to get:
19 * x + 11 * y = 17 * x + 17 * y
subtract the right side of the equation from both sides of the equation to get:
19 * x - 17 * y + 11 * y - 17 * y = 0
combine like terms to get:
2 * x - 6 * y = 0
your two equations become:
x + y = 16
2 * x - 6 * y = 0
multiply both sides of the first equation by 2 and leave the second equation as is to get:
2x + 2y = 32
2x - 6y = 0
subtract the second equation from the first to get:
8y = 32
solve for y to get:
y = 32/8 = 4
in the first equation, replace y with 4 to get:
x + y = 16 becomes x + 4 = 16
solve for x to get:
x = 16 - 4 = 12
you have:
x = 12
y = 4
first equation of x + y = 16 becomes 12 + 4 = 16 which becomes 16 = 16.
second equation of 19x + 11y = 17(x + y) becomes:
19*12 = 11*4 = 17 * 16 which becomes 272 = 272.
the values of x = 12 and y = 4 appear to be good.
you take 12 pounds of indonesiann cinnamon, which is 19 dollars a pound, and mix it with 4 pounds of thai cinnamon, which is 11 dollars a pound, you will get 16 pounds of brand M cinnamon which costs (19 * 12 + 11 * 4) / 16 = 17 dollars a pound.
your solution is that you used 12 pounds of indonesian cinnamon and 4 pounds of thai cinnamon.
The solution from the other tutor is fine. But nearly always an algebraic solution is easier if you set up the problem using a single variable.
x = pounds of Indonesian cinnamon at $19/lb
16-x = pounds of Thai cinnamon at $11/lb
The 16 pounds mixture costs $17/lb:
ANSWER:
Indonesian cinnamon: x=12 pounds
Thai cinnamon: 16-x=4 pounds
CHECK: 19(12)+11(4)=228+44=272
Presumably this problem is to be solved by a student who is just learning how to use algebra to solve problems, so a formal algebraic solution like the one above is what was wanted.
However, if a formal algebraic solution is not required, the answer to any 2-part mixture problem like this can be found quickly with a bit of easy mental arithmetic.
(1) Observe/calculate that the $17 per pound cost of the mixture is 3/4 of the way from the $11 per pound cost of the Thai cinnamon to the $19 per pound cost of the Indonesian cinnamon.
(2) That means 3/4 of the mixture is the more expensive cinnamon.
ANSWER: 3/4 of 16 pounds, or 12 pounds, of Indonesian cinnamon, the other 4 pounds of Thai cinnamon.
