Question 160271
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.