Q. A farmers in Alberta often deliver wheat to grain elevators using grain truck, which are a type of dump truck.
A farmer make two trips to a grain elevator. The grain elevator manager measures the combined mass of the farmer's truck and wheat in tonnes (t), and then calculates the bushels of wheat dumped from the truck
Table:
Combined Mass of truck and wheat (t):
16.2
21.6
Bushels of Wheat (Bu):
300
500
a) write a linear equation to represent this situation. Use this equation to determine the combined mass of the truck and the wheat in tonnes when the truck is loaded with 600 bushels of wheat.
b. Use the equation to determine the mass of the farmer's truck in tonnes.
I having hard time doing this question when it come to word problem. Can someone please help me?
Thank You very much!!!!
if x is the combined mass of truck and wheat, and b is the # bushels, then
b-300 = (500-300)/(21.6-16.2) (x-16.2)
b = 37.037x - 300
so, find x when b=600
Now, if the truck weighs t and each bushel of wheat weighs w, we have
t + 300w = 16.2
t + 500w = 21.6
so, w = 0.027, and t = 8.1
So, the truck weighs 8.1 tonnes
Thank You So much, I appreciate the help
a) To write a linear equation, we need to find the relationship between the combined mass of the truck and wheat (in tonnes) and the bushels of wheat dumped from the truck.
Let's define the combined mass of the truck and wheat as "m" (in tonnes), and the bushels of wheat dumped as "b".
From the given data, we have the following points:
(16.2, 300) and (21.6, 500)
Now, we can find the slope (m) using the formula:
m = (change in y) / (change in x)
m = (500 - 300) / (21.6 - 16.2)
m = 200 / 5.4
m = 37.04
Now, we can use the point-slope form of a linear equation to find the equation:
y - y1 = m(x - x1)
Using the first point (16.2, 300):
y - 300 = 37.04(x - 16.2)
Simplifying the equation:
y - 300 = 37.04x - 597.648
y = 37.04x - 297.648
This equation represents the relationship between the combined mass (m) and the bushels of wheat dumped (b).
To determine the combined mass of the truck and wheat in tonnes when the truck is loaded with 600 bushels of wheat, we substitute the value of 600 for y (b) in the equation:
600 = 37.04x - 297.648
Solving for x (m):
37.04x = 897.648
x = 897.648 / 37.04
x ≈ 24.23
Therefore, the combined mass of the truck and wheat is approximately 24.23 tonnes when the truck is loaded with 600 bushels of wheat.
b) To determine the mass of the farmer's truck in tonnes, we need to subtract the mass of the wheat from the combined mass.
Using the second point (21.6, 500):
500 = 37.04x - 297.648
37.04x = 797.648
x = 797.648 / 37.04
x ≈ 21.5
Therefore, the mass of the farmer's truck is approximately 21.5 tonnes.
Sure! I can help you with this question.
To solve this problem, we need to determine the linear relationship between the combined mass of the truck and wheat (in tonnes) and the number of bushels of wheat dumped from the truck.
Let's start by finding the slope of the line. Slope is the change in y (bushels) divided by the change in x (combined mass of the truck and wheat).
Using the given values from the table:
Change in y = 500 - 300 = 200 bushels
Change in x = 21.6 - 16.2 = 5.4 tonnes
Slope = change in y / change in x = 200 / 5.4 = 37.037
Next, we need to find the y-intercept, which is the value of y when x is zero. Looking at the table, we can see that when the combined mass is zero, the bushels are also zero. Therefore, the y-intercept is zero.
Now we can write the linear equation using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
The equation is: y = 37.037x
a) To determine the combined mass when the truck is loaded with 600 bushels of wheat, we can substitute 600 for y in the equation and solve for x (the combined mass).
600 = 37.037x
x = 600 / 37.037 ≈ 16.21 tonnes
Therefore, when the truck is loaded with 600 bushels of wheat, the combined mass of the truck and wheat is approximately 16.21 tonnes.
b) To determine the mass of the farmer's truck in tonnes, we need to find the value of x (the combined mass) when y (the bushels) is zero.
0 = 37.037x
x = 0
Therefore, the mass of the farmer's truck is zero tonnes.
I hope this helps clarify the problem and guide you through the solution! Let me know if you have any further questions.