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!!!!
Sure! I can help you with that. Let's go step by step.
a) To write a linear equation that represents this situation, 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 use the formula for the equation of a line, which is:
y = mx + b
In this case, the "y" variable represents the combined mass of the truck and wheat in tonnes, and the "x" variable represents the bushels of wheat dumped from the truck. So we need to find the values of "m" and "b" to complete the equation.
We are given two sets of data:
Combined Mass of truck and wheat (t): 16.2, 21.6
Bushels of Wheat (Bu): 300, 500
To find "m," which represents the slope of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the values from the data, we can calculate the slope:
m = (21.6 - 16.2) / (500 - 300)
m = 5.4 / 200
m = 0.027
Now, to find "b," which represents the y-intercept of the line, we can use the formula:
b = y - mx
Using one set of data (let's use the first set), we can substitute the values into the equation:
b = 16.2 - (0.027 * 300)
b = 16.2 - 8.1
b = 8.1
Therefore, the linear equation representing this situation is:
y = 0.027x + 8.1
Now, we can use this equation to determine the combined mass of the truck and wheat in tonnes when the truck is loaded with 600 bushels of wheat.
Substituting x = 600 into the equation:
y = 0.027 * 600 + 8.1
y = 16.2 + 8.1
y = 24.3
Therefore, the combined mass of the truck and wheat in tonnes when the truck is loaded with 600 bushels of wheat is 24.3 tonnes.
b) We can also use the equation to determine the mass of the farmer's truck in tonnes.
Since the truck's mass is the y-intercept of the line, we can directly read it from the equation.
The mass of the farmer's truck in tonnes is 8.1 tonnes.
I hope this helps! Let me know if you have any further questions.
Sure! I can help you with this problem. To solve this question, we first need to find the linear equation that represents the relationship between the combined mass of the truck and wheat and the bushels of wheat dumped from the truck.
Let's analyze the given data in the table:
Combined Mass of truck and wheat (t):
16.2
21.6
Bushels of Wheat (Bu):
300
500
To find the equation, we can use the equation of a straight line, which is y = mx + b, where y represents the bushels of wheat and x represents the combined mass of the truck and wheat.
To find the slope (m) of the line, we use the formula: (change in y) / (change in x).
Slope (m) = (500 - 300) / (21.6 - 16.2) = 200 / 5.4 = 37.037 t/Bu.
Now, let's substitute one of the points from the table into the equation to find the y-intercept (b).
Using the point (16.2, 300):
300 = (37.037)(16.2) + b
300 = 597.8814 + b
b = 300 - 597.8814
b ≈ -297.8814 t
So, the equation that represents this situation is:
y = 37.037x - 297.8814
Now, we can use this equation to determine the combined mass of the truck and wheat in tonnes when the truck is loaded with 600 bushels of wheat:
Let x be the combined mass of the truck and wheat when the truck is loaded with 600 bushels of wheat.
600 = 37.037x - 297.8814
Add 297.8814 to both sides of the equation:
897.8814 = 37.037x
Now, divide both sides by 37.037 to solve for x:
x ≈ 24.23 t
Therefore, when the truck is loaded with 600 bushels of wheat, the combined mass of the truck and wheat is approximately 24.23 tonnes.
For part b, we need to determine the mass of the farmer's truck in tonnes:
We can use the equation: y = 37.037x - 297.8814.
Since the y in this case represents the bushels of wheat, we can substitute the given value of bushels (300) into the equation and solve for x:
300 = 37.037x - 297.8814
Add 297.8814 to both sides of the equation:
597.8814 = 37.037x
Now, divide both sides by 37.037 to solve for x:
x ≈ 16.14 t
Therefore, the mass of the farmer's truck is approximately 16.14 tonnes.