Question
Month after month, Paula is in charge of paying the water bill in her house. In a given month, they consumed 8 cubic meters of water, paying a total of $8,060. The following month, they used 11 cubic meters, having to pay an amount of $10,820. Paula realized that in both months she was charged a fixed charge in addition to the cost for each cubic meter of water consumed. To calculate how much she will have to pay in the coming months, Paula needs to determine the function f that relates the water consumption in cubic meters to the total amount to pay, including the fixed charge. What would be the function that Paula should use to calculate the amount to pay based on water consumption?
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Answer to a math question Month after month, Paula is in charge of paying the water bill in her house. In a given month, they consumed 8 cubic meters of water, paying a total of $8,060. The following month, they used 11 cubic meters, having to pay an amount of $10,820. Paula realized that in both months she was charged a fixed charge in addition to the cost for each cubic meter of water consumed. To calculate how much she will have to pay in the coming months, Paula needs to determine the function f that relates the water consumption in cubic meters to the total amount to pay, including the fixed charge. What would be the function that Paula should use to calculate the amount to pay based on water consumption?
Eliseo
4.6110 Answers
1. Set up the system of linear equations using the given data points:
\begin{cases} 8m + b = 8060 \\ 11m + b = 10820 \end{cases}
2. Subtract the first equation from the second to eliminateb
11m + b - (8m + b) = 10820 - 8060
3m = 2760
m = 920
3. Substitutem = 920 b
8(920) + b = 8060
7360 + b = 8060
b = 700
4. The linear function relating the water consumption to the total amount to pay is:
f(x) = 920x + 700
2. Subtract the first equation from the second to eliminate
3. Substitute
4. The linear function relating the water consumption to the total amount to pay is:
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