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A cannery processed 1,445 pounds of strawberries in 4.5 hours. The cannery processed 2,320 pounds in 8 hours.
Write a linear equation to model the relationship between the weight of strawberries S and time T.
How many pounds of strawberries can be processed in 11 hours?
To write a linear equation to model the relationship between the weight of strawberries S and time T, we can use the formula for a linear equation: y = mx + b, where y represents the weight of strawberries (S), x represents the time (T), m represents the slope, and b represents the y-intercept.
To find the slope, we can use the formula:
slope (m) = (change in y) / (change in x)
Given that the cannery processed 1,445 pounds of strawberries in 4.5 hours and 2,320 pounds in 8 hours, we can calculate the slope as follows:
slope (m) = (2,320 - 1,445) / (8 - 4.5) = 875 / 3.5 = 250
Now that we have the slope, we can find the y-intercept (b) using one of the given data points. Let's use the data point (4.5, 1445):
1445 = 250 * 4.5 + b
1445 = 1125 + b
b = 1445 - 1125
b = 320
So, the linear equation that models the relationship between the weight of strawberries S and time T is:
S = 250T + 320
To find how many pounds of strawberries can be processed in 11 hours, we substitute T = 11 into the equation:
S = 250 * 11 + 320
S = 2750 + 320
S = 3070
Therefore, 3,070 pounds of strawberries can be processed in 11 hours.
To write a linear equation to model the relationship between the weight of strawberries S and time T, we can use the concept of a slope-intercept form of a linear equation, which is given by the equation:
y = mx + b
Here, y represents the weight of strawberries (S), x represents the time (T), m represents the slope of the line, and b represents the y-intercept.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the given information, we can choose two points (x1, y1) and (x2, y2) that lie on the line. Let's use the points (4.5, 1445) and (8, 2320).
m = (2320 - 1445) / (8 - 4.5)
m = 875 / 3.5
m = 250
So, the slope (m) is 250.
Now, to find the y-intercept (b), we can substitute the coordinates of one of the points into the equation:
1445 = 250 * 4.5 + b
1445 = 1125 + b
b = 1445 - 1125
b = 320
So, the y-intercept (b) is 320.
The linear equation that models the relationship between the weight of strawberries S and time T is:
S = 250T + 320
To find how many pounds of strawberries can be processed in 11 hours, we can substitute T = 11 into the equation:
S = 250 * 11 + 320
S = 2750 + 320
S = 3070
Therefore, in 11 hours, 3,070 pounds of strawberries can be processed.
To write a linear equation to model the relationship between the weight of strawberries S and time T, we can use the formula for the equation of a line:
y = mx + b
In this case, y represents the weight of strawberries (S) and x represents the time (T).
First, we can find the slope (m) using the given data points (2,320 pounds in 8 hours and 1,445 pounds in 4.5 hours). The slope is calculated as the change in y divided by the change in x:
m = (y2 - y1) / (x2 - x1)
m = (2,320 - 1,445) / (8 - 4.5)
m = 875 / 3.5
m = 250
Next, we can choose one of the data points to substitute into the equation to find the y-intercept (b). Let's use the point (4.5, 1,445):
1,445 = 250 * 4.5 + b
1,445 = 1,125 + b
b = 1,445 - 1,125
b = 320
Now we can write the linear equation:
S = 250T + 320
To find how many pounds of strawberries can be processed in 11 hours, we substitute T = 11 into the equation:
S = 250 * 11 + 320
S = 2,750 + 320
S = 3,070
Therefore, in 11 hours, the cannery can process 3,070 pounds of strawberries.