James bought 14 big and 'small boxes öf oranges. Each big box contained 50 oranges and each small box contained 30 oranges. If he bought 520 oranges altogether, how many big boxes and how many small boxes of oranges did he buy?
Let's say James bought b big boxes.
Since each big box contains 50 oranges, the total number of oranges in the big boxes is 50 * b = 50b.
James also bought s small boxes.
Since each small box contains 30 oranges, the total number of oranges in the small boxes is 30 * s = 30s.
The total number of oranges James bought is 50b + 30s = 520.
Since each big box contained 50 oranges, the total number of oranges in the big boxes is 50 * b = 50b.
Since each small box contained 30 oranges, the total number of oranges in the small boxes is 30 * s = 30s.
The total number of oranges James bought is the sum of the number of oranges in the big and small boxes: 50b + 30s = 520.
There are two equations, 50b + 30s = 520 and b + s = 14, to represent the total number of oranges in the boxes and the total number of boxes, respectively.
To simplify the equations, divide both sides of the first equation by 10 to get 5b + 3s = 52.
Then subtract the equation b + s = 14 from the two equations to get 5b - b + 3s - s = 52 - 14.
This simplifies to 4b + 2s = 38.
Divide both sides of the equation by 2 to get 2b + s = 19.
Next, subtract the equation 2b + s = 19 from the equation 5b + 3s = 52 to get 5b - 2b + 3s - s = 52 - 19.
This simplifies to 3b + 2s = 33.
Solve the two equations 2b + s = 19 and 3b + 2s = 33 simultaneously to find the values of b and s.
Multiply the first equation by 3 to get 6b + 3s = 57.
Next, subtract the second equation from the first equation to get 6b + 3s - (3b + 2s) = 57 - 33.
Simplify the expression to get 6b + 3s - 3b - 2s = 24.
Combine like terms to get 3b + s = 24.
To solve the equations 2b + s = 19 and 3b + 2s = 33 simultaneously, first solve the equation 3b + s = 24 for s to get s = 24 - 3b.
Substitute the value of s in the equation 2b + s = 19 to get 2b + 24 - 3b = 19.
Combine like terms to get -b + 24 = 19.
Subtract 24 from both sides of the equation to get -b = 19 - 24.
Simplify to get -b = -5.
Multiply both sides of the equation by -1 to get b = 5.
Substitute the value of b in the equation s = 24 - 3b to get s = 24 - 3 * 5 = 24 - 15 = 9.
James bought 5 big boxes and 9 small boxes. Answer: \boxed{5, 9}.
Let's assume that James bought x big boxes and y small boxes of oranges.
The number of oranges in the big boxes would be 50x, and the number of oranges in the small boxes would be 30y.
According to the given information, James bought a total of 14 boxes of oranges, so we have the following equation:
x + y = 14 ---(1)
The total number of oranges that James bought is 520, so we have another equation:
50x + 30y = 520 ---(2)
Now we can solve these two equations simultaneously to find the values of x and y.
Let's multiply equation (1) by 30 to eliminate y:
30x + 30y = 420 ---(3)
Now we can subtract equation (3) from equation (2):
50x + 30y - (30x + 30y) = 520 - 420
Simplifying this equation, we get:
20x = 100
Dividing both sides of the equation by 20, we find:
x = 5
Now we can substitute this value of x back into equation (1) to find the value of y:
5 + y = 14
Subtracting 5 from both sides of the equation, we get:
y = 9
Therefore, James bought 5 big boxes and 9 small boxes of oranges.