SOLUTION: A glue company needs to make some glue tat it can sell at $120 per barrel.It wants to use 150 barrels of glue worth $100 per barrel, along with glue worth $150 per barrel and and g

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Question 419129: A glue company needs to make some glue tat it can sell at $120 per barrel.It wants to use 150 barrels of glue worth $100 per barrel, along with glue worth $150 per barrel and and glue worth $190 per barrel.It must use the same number of barrels of $150 and $190 glue.How much of the $150 and $190 glue will be needed?How many Barrels of $120 glue will be produced?
Found 4 solutions by mananth, ikleyn, greenestamps, josgarithmetic:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!
$100 -----150barrels
$150------- x
$190-------x

Mix $120 = 150+2x
100*150+150x+190x=120(150+2x)
15000+340x=300x+18000
40x=3000
x=75 barrels $150 & $190

Answer by ikleyn(53751)   (Show Source):
You can put this solution on YOUR website!
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A glue company needs to make some glue tat it can sell at $120 per barrel.
It wants to use 150 barrels of glue worth $100 per barrel, along with glue worth $150 per barrel
and glue worth $190 per barrel.
It must use the same number of barrels of $150 and $190 glue.
How much of the $150 and $190 glue will be needed? How many Barrels of $120 glue will be produced?
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        The solution and the answer in the post by @mananth both are incorrect.
        I came to bring a correct solution.

$100 -----150barrels
$150------- x
$190-------x

Mix $120 = 150+2x
100*150 + 150x + 190x = 120*(150 + 2x)
15000 + 340x = 240x + 18000
100x = 3000
x = 30 barrels at $150 and $190.     <<<---===   ANSWER

Solved correctly.

Answer by greenestamps(13327)   (Show Source):
You can put this solution on YOUR website!

Another tutor has provided a standard formal algebraic solution to the problem. But the numbers in this problem make it a good one for solving informally using logical reasoning instead of formal algebra.

Since equal amounts of the glues worth $150 per barrel and $190 per barrel are to be used, the average cost of those two ingredients is halfway between those two prices, which is $170 per barrel.

Then the problem becomes mixing glue worth $100 per barrel with glue worth $170 per barrel to get glue worth $120 per barrel. The ratio in which those two ingredients must be mixed is exactly determined by where the $120 price lies between the $100 and $170 prices.

The difference between $100 and $120 is $20; the difference between $120 and $170 is $50. Those differences mean the two ingredients must be mixed in the ratio 20:50 = 2:5.

Because $120 is closer to $100 than it is to $170, the larger portion must be the ingredient worth $100 per barrel. So the mixture needs to be 5 parts of the glue worth $100 per barrel and 2 parts of the glue worth $170 per barrel.

Given that there are 150 barrels of glue worth $100 per barrel, use a proportion to find that we need 60 barrels of the glue worth $170 per barrel:

Then, since the glue worth $170 per barrel is equal amounts of the glues worth $150 and $190 per barrel, there must be 30 barrels each of the $150 per barrel glue and the $190 per barrel glue.

ANSWERS:
(1) 30 barrels each of the $150 per barrel and $190 per barrel glue will be used
(2) The total number of barrels of glue will be 150+30+30 = 210

Answer by josgarithmetic(39792)   (Show Source):
You can put this solution on YOUR website!

PRICE VOLUME-barrels COST 100 150 15000 150 v 150v 190 v 190v ----------------------------------------------- 120 2v+150 340v+15000

Result mix must be 120 dollars per barrel.

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