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Answer :
Certainly! Let's solve the problem step-by-step.
We need to find the correct equation that relates the temperatures in Miami, Florida, and Bangor, Maine, based on the given information:
1. Information Given:
- The temperature in Miami is 82 degrees.
- The temperature in Miami is 22 degrees warmer than three times the temperature in Bangor, Maine.
2. Assign a Variable:
- Let's denote the temperature in Bangor, Maine, as [tex]\( x \)[/tex].
3. Set Up the Equation:
- Since Miami's temperature is 22 degrees warmer than three times Bangor's temperature, we can write this as:
[tex]\[
\text{Temperature in Miami} = 3 \times (\text{Temperature in Bangor}) + 22
\][/tex]
4. Substitute the Known Values:
- We know the temperature in Miami is 82 degrees. So the equation becomes:
[tex]\[
82 = 3x + 22
\][/tex]
5. Solve the Equation:
- Start by isolating [tex]\( 3x \)[/tex] on one side of the equation:
[tex]\[
82 - 22 = 3x
\][/tex]
[tex]\[
60 = 3x
\][/tex]
- Now, solve for [tex]\( x \)[/tex] by dividing both sides by 3:
[tex]\[
x = \frac{60}{3}
\][/tex]
[tex]\[
x = 20
\][/tex]
So, the temperature in Bangor, Maine, is 20 degrees. Therefore, the correct equation from the options is:
[tex]\[ 3x + 22 = 82 \][/tex]
This option represents the initial setup of the problem where Miami's temperature is 22 degrees warmer than three times Bangor's temperature.
We need to find the correct equation that relates the temperatures in Miami, Florida, and Bangor, Maine, based on the given information:
1. Information Given:
- The temperature in Miami is 82 degrees.
- The temperature in Miami is 22 degrees warmer than three times the temperature in Bangor, Maine.
2. Assign a Variable:
- Let's denote the temperature in Bangor, Maine, as [tex]\( x \)[/tex].
3. Set Up the Equation:
- Since Miami's temperature is 22 degrees warmer than three times Bangor's temperature, we can write this as:
[tex]\[
\text{Temperature in Miami} = 3 \times (\text{Temperature in Bangor}) + 22
\][/tex]
4. Substitute the Known Values:
- We know the temperature in Miami is 82 degrees. So the equation becomes:
[tex]\[
82 = 3x + 22
\][/tex]
5. Solve the Equation:
- Start by isolating [tex]\( 3x \)[/tex] on one side of the equation:
[tex]\[
82 - 22 = 3x
\][/tex]
[tex]\[
60 = 3x
\][/tex]
- Now, solve for [tex]\( x \)[/tex] by dividing both sides by 3:
[tex]\[
x = \frac{60}{3}
\][/tex]
[tex]\[
x = 20
\][/tex]
So, the temperature in Bangor, Maine, is 20 degrees. Therefore, the correct equation from the options is:
[tex]\[ 3x + 22 = 82 \][/tex]
This option represents the initial setup of the problem where Miami's temperature is 22 degrees warmer than three times Bangor's temperature.
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