Question 160271: A market vendor wants to mix the liver and the gizzards of chickens to have 40 kilograms of assortment worth 120.00 per kilogram. The liver costs 110.00 per kilogram while the gizzard costs 75.00 per kilogram. How much each kind must be mixed?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! something appears to be wrong with your equation.
the composite value of L+G) can't be 120 * (L+G) since none of the piece parts has a value greater than 120.
you have 110*L and you have 75*G
if you have all L, then you have 40 * 110
if you have all G, then you have 40 * 75
neither of these will ever get to be as high as 120 * (L+G)
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let's do the problem with a value for (L+G) that will work.
something between 75 and 110.
let's try 90
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now we should be able to solve
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let L = liver of chickens
let G = gizzards of chickens
total weight of liver and gizzards is 40 kg, so
L + G = 40
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value of L is 110 per kg
value of G is 75 per kg
value of total is 90 per kg
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equation for value becomes
110*L + 75*G = 90*40
this becomes 110*L + 75*G = 3600
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now you have 2 simultaneous equations you need to solve. they are
L + G = 40
110*L + 75*G = 3600
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solve for L in the first equation
L = 40 - G
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substitute 40 - G for L in the second equation. it becomes
110 * (40 - G) + 75 * G = 3600
which becomes
(110*40) - (110*G) + 75*G = 3600
which becomes
4400 - 110*G + 75*G = 3600
which becomes
4400 - 35*G = 3600
subtracting 3600 from both sides of the equation and adding 35*G to both sides of the equation and it becomes
4400 - 3600 = 35*G
which becomes
800 = 35*G
dividing both sides of the equation by 35 and it becomes
22.857.... = G
substituting for G in the first equation and it becomes
L + 22.857... = 40
which becomes
L = 40 - 22.857...
which becomes L = 17.1428...
substituting 22.857... for G and 17.1428... for L in the second equation and it becomes
110*(17.1428...) + 75*(22.857...) = 3600
calculating out we get 3600 = 3600
the answer of
L = 17.1428...
G = 22.857...
is correct.
i used the values stored in the calculator which go out further than 17.1428.
this is why i showed 17.1428 as 17.1428...
if you try to duplicate this, use the numbers stored in the calculator.
the answer will then be correct, or much closer to correct.
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as indicated earlier, the value of 120*40 will not work because you cannot get 120*40 from any combination of 110*L and 75*G.
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