Let the price of a chicken be represented as x and the price of a duck as y. The equations established are 50x + 30y = 550 (1) and 44x + 36y = 532 (2). By manipulating (1) with a factor of 6, we have 300x + 180y = 3,300 (3). Applying a factor of 5 to (2) results in 220x + 180y = 2,660 (4). Then, by subtracting (4) from (3), we find that 80x = 640, leading to x = 8. Substituting the value of x back into (1), we find 50(8) + 30y = 550, which simplifies to 30y = 150, and ultimately y = 5. Therefore, the costs are $8 for a chicken and $5 for a duck.
The equation that demonstrates a proportional relationship, maintaining a constant of proportionality equal to 14, is: Here, and are proportional with a constant of proportionality of 14.
