Final answer:
To find the weight of a 50-passenger bus, we can use a linear equation. The equation w = (1/8)p + 2.5 is used to find the weight (w) based on the seating capacity (p). Substituting p = 50 into the equation gives a weight of 8.75 tons.
Step-by-step explanation:
To find the weight of a 50-passenger bus, we can use the given information to set up a linear equation. Let's assume that the weight of the bus is represented by w in tons and the seating capacity is represented by p.
We are given two data points: a 60-passenger bus weighs 10 tons and an 84-passenger bus weighs 13 tons. Using these data points, we can set up a linear equation:
(60, 10) and (84, 13)
The formula for a linear equation is y = mx + b, where y is the dependent variable (weight in this case), x is the independent variable (seating capacity), m is the slope of the line, and b is the y-intercept.
Using the two data points, we can find the slope:
m = (13 - 10) / (84 - 60) = 3 / 24 = 1/8
Now that we have the slope, we can find the y-intercept by plugging in one of the data points. Using (84, 13):
13 = (1/8)(84) + b
b = 13 - (1/8)(84) = 13 - 10.5 = 2.5
So, the equation for the weight of the bus (w) based on the seating capacity (p) is:
w = (1/8)p + 2.5
To find the weight of a 50-passenger bus, we simply substitute p = 50 into the equation:
w = (1/8)(50) + 2.5 = 6.25 + 2.5 = 8.75
Therefore, the weight of a 50-passenger bus is 8.75 tons.