To write a linear equation to model the relationship between the weight of strawberries S and time T, we need to find the rate at which strawberries are processed.
For the first scenario, processing 1,445 pounds of strawberries in 4.5 hours, the rate of processing is:
(1,445 pounds)/(4.5 hours) = 321.11111 pounds/hour (round to 5 decimal places)
For the second scenario, processing 2,320 pounds in 8 hours, the rate of processing is:
(2,320 pounds)/(8 hours) = 290 pounds/hour (rounded to the nearest whole number)
To find the equation, we need the equation of a line in the form of y = mx + b, where y is the weight of strawberries, x is the time, m is the rate of processing, and b is the y-intercept.
Using the rate of processing from the second scenario (290 pounds/hour), we can write the equation as:
S = 290T + b
To find the y-intercept (b), we can use the first scenario. Substituting the weight (1,445 pounds) and time (4.5 hours) into the equation:
1,445 = 290(4.5) + b
1,445 = 1,305 + b
b = 1,445 - 1,305
b = 140
Therefore, the equation to model the relationship between the weight of strawberries S and time T is:
S = 290T + 140
To find the weight of strawberries that can be processed in 11 hours, we can substitute T = 11 into the equation:
S = 290(11) + 140
S = 3,190 + 140
S = 3,330
Therefore, 3,330 pounds of strawberries can be processed in 11 hours.
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?
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