An 8 liter can filled with cooking oil weights 42kg. When 5 liters are emptied from the can,the can and the oil weight 27kg.What is the weight of the empty can?
weight of cooking oil per litre ---- x kg
weight of can ---- y kg
8x + y = 42
3x + y = 27
subtract them
5x = 15
x = 3
sub into 3x + y = 27
9 + y = 27
y = 18
the empty can weighs 18 kg
check:
8(3) + 18 = 42
3(3) + 18 = 27
my answer is correct
To solve this problem, we need to use a system of equations. Let's denote the weight of the empty can as "x" kg.
According to the problem, the 8-liter can filled with cooking oil weighs 42 kg. We can write this as:
Oil weight + Can weight = Total weight
42 kg = Oil weight + x kg
When 5 liters are emptied from the can, the can and the oil weigh 27 kg. We can write this as:
(8 - 5) liters of oil weight + Can weight = Total weight
27 kg = (8 - 5) liters of oil weight + x kg
Simplifying the second equation, we get:
27 kg = 3 liters of oil weight + x kg
Now we have a system of equations:
42 kg = Oil weight + x kg
27 kg = 3 liters of oil weight + x kg
To solve this system, we can subtract the second equation from the first equation:
42 kg - 27 kg = (Oil weight - 3 liters of oil weight) + (x kg - x kg)
15 kg = -2 liters of oil weight
Now we can solve for the weight of one liter of oil by dividing both sides of the equation by -2:
15 kg / -2 = -2 liters of oil weight / -2
-7.5 kg = 1 liter of oil weight
Since the weight of the empty can is x kg, and the weight of 5 liters of oil is (-7.5 kg * 5 liters), we can substitute these values back into the second equation to solve for x:
27 kg = 3 liters of oil weight + x kg
27 kg = 3 (-7.5 kg) + x kg
27 kg = -22.5 kg + x kg
Let's isolate x by subtracting -22.5 kg from both sides of the equation:
27 kg - (-22.5 kg) = -22.5 kg + x kg - (-22.5 kg)
49.5 kg = x kg
Therefore, the weight of the empty can is 49.5 kg.