find the worlds production of nickel in a year when russia and new caledonia together produced 1/3 of it,canada 1/6 of it,and australia 1/9 of it, and the rest of the world 420,000 tons.
find the worlds production of nickel in a year when russia and new caledonia together produced 1/3 of it,canada 1/6 of it,and australia 1/9 of it, and the rest of the world 420,000 tons.
Let x = world production
1/3 x + 1/6 x +1/9 x = x - 420,000
Solve for x.
I hope this helps.
To find the world's production of nickel in a year, we first need to determine the production amounts for Russia, New Caledonia, Canada, and Australia.
Let's assign variables to represent the production amounts:
Let R = production of nickel by Russia,
N = production of nickel by New Caledonia,
C = production of nickel by Canada, and
A = production of nickel by Australia.
We know that Russia and New Caledonia together produced 1/3 of the world's production, Canada produced 1/6, and Australia produced 1/9. The rest of the world produced 420,000 tons.
So, according to the given information, we can write the following equations:
R + N = 1/3 * X (equation 1)
C = 1/6 * X (equation 2)
A = 1/9 * X (equation 3)
R + N + C + A = X - 420,000 (equation 4)
Here, X represents the total world production of nickel.
To solve this system of equations, we will use a substitution method:
From equation 2, we have C = 1/6 * X.
Substituting this value into equation 4, we get:
R + N + 1/6 * X + A = X - 420,000.
Similarly, using equation 3, we have A = 1/9 * X.
Substituting this value into the above equation, we get:
R + N + 1/6 * X + 1/9 * X = X - 420,000.
Combining like terms, we have:
R + N + 5/18 * X = X - 420,000.
To get rid of the fractions, we can multiply both sides of the equation by 18:
18R + 18N + 5X = 18X - 7,560,000.
Now, let's rewrite equation 1 in terms of X:
R + N = 1/3 * X
Multiplying both sides by 3 to eliminate the fraction:
3R + 3N = X.
We can substitute this value into the previous equation:
18R + 18N + 5X = 18X - 7,560,000
18(X) + 5X = 18(X) - 7,560,000
23X = 18X - 7,560,000
5X = -7,560,000
X = -7,560,000 / 5
X = -1,512,000.
The value we obtained for X is negative, which seems illogical. There might be a mistake in the given information or calculations. Please double-check the provided numbers to ensure accuracy.