The temperature of a city changed by a total of −15 degrees Celsius over a 5-week period. The temperature changed by the same amount each week.
Part A: Write an expression to show the average change in the temperature of the city each week. (5 points)
Part B: Simplify the expression and explain, using words, what your answer means.
You need to write this in a paragraph.
Part A: Let's represent the average change in the temperature of the city each week as 'x'. Since the temperature changed by the same amount each week and decreased by a total of 15 degrees Celsius over 5 weeks, the expression for the average change in temperature per week can be written as: x = -15/5.
Part B: To simplify the expression, we perform the division: x = -15/5 = -3. This means that on average, the temperature of the city decreased by 3 degrees Celsius every week. The negative sign indicates a decrease in temperature. Therefore, the average change in the temperature of the city per week is a decrease of 3 degrees Celsius.
Part A: To find the average change in temperature each week, we can divide the total change in temperature (-15 degrees Celsius) by the number of weeks (5 weeks). Let's denote the average change in temperature per week as "x." Therefore, the expression to represent the average change in temperature per week would be:
Average change per week = -15 degrees Celsius / 5 weeks = -3 degrees Celsius/week.
Part B: By simplifying the expression, we find that the average change in temperature each week is -3 degrees Celsius. This means that the temperature of the city decreases by 3 degrees Celsius every week, on average, over the 5-week period. The negative sign indicates a decrease in temperature, and the magnitude represents the amount of change. Thus, the average change in temperature per week is a decrease of 3 degrees Celsius.
Part A: To find the average change in temperature per week, we can take the total change in temperature over 5 weeks and divide it by the number of weeks. Let's call the average change in temperature per week "x". Since the temperature changed by the same amount each week, we know that the total change over 5 weeks is -15 degrees Celsius. Therefore, our expression would be: x = -15 / 5.
Part B: To simplify the expression -15/5, we can divide the numerator (which is -15) by the denominator (which is 5). This yields -3 as the result. In words, the answer means that the average change in temperature of the city each week is -3 degrees Celsius. This indicates that the temperature decreases by 3 degrees Celsius on average every week over the 5-week period.