Question

City A and City B had two different temperatures on a particular day. On that day, five times the temperature of City A was 8° C more than three times the temperature of City B. The temperature of City A minus twice the temperature of City B was −4° C. The following system of equations models this scenario:

Answer 1

To convert a 40.0°F temperature decrease to Celsius, subtract 32 and multiply by 5/9, resulting in a 22.2°C decrease. The change in Fahrenheit is nine-fifths the change in Celsius. When considering heat requirements, each degree Celsius is equivalent to 1.8 degrees Fahrenheit.

Step-by-step explanation:

Understanding Temperature Conversion

The question relates to the conversion of temperature units between Fahrenheit and Celsius. When the temperature decreases by 40.0°F, the corresponding decrease in degrees Celsius can be calculated using the formula ∆C = (∆F - 32) × 5/9, where ∆F is the change in Fahrenheit temperature. Applying this formula, a 40.0°F decrease is equivalent to a 22.2°C decrease in temperature.

To show that any change in temperature in Fahrenheit degrees is nine-fifths the change in Celsius degrees, we use the direct relationship between the two scales: ∆F = ∆C × 9/5. This relationship indicates that for every degree of change in Celsius, there is a 9/5 degree change in Fahrenheit.

When discussing heat requirements for containers, it is important to note that the conversion factor between Celsius and Fahrenheit is 1.8. This means that each degree Celsius increase requires an increase of 1.8 degrees Fahrenheit to maintain equivalent temperatures.

Answer 2

Answer: Let x be the temperature in degrees Celsius of City A on that day, and let y be the temperature in degrees Celsius of City B on that day. Then the system of equations that models this scenario is:

5x = 3y + 8 (Equation 1)

x - 2y = -4 (Equation 2)

The first equation represents the fact that five times the temperature of City A was 8° C more than three times the temperature of City B. The second equation represents the fact that the temperature of City A minus twice the temperature of City B was −4° C.

We can solve for one of the variables in terms of the other variable by rearranging one of the equations. For example, we can solve for x in Equation 2:

x = 2y - 4

We can substitute this expression for x into Equation 1:

5(2y - 4) = 3y + 8

Simplifying and solving for y:

10y - 20 = 3y + 8

7y = 28

y = 4

Now that we know the temperature of City B was 4°C, we can substitute this value for y in Equation 2 to solve for x:

x - 2(4) = -4

x - 8 = -4

x = 4

So the temperature of City A was also 4°C.

Therefore, on that day, City A and City B had temperatures of 4°C and 4°C, respectively.

Step-by-step explanation: