Answer :
To solve the problem, let's determine the equation that represents the relationship between the temperatures in Miami and Bangor.
1. Define Variables:
- Let's let `x` represent the temperature in Bangor, Maine.
2. Understand the Relationship:
- The temperature in Miami is described as being 22 degrees warmer than three times the temperature in Bangor.
3. Write the Equation:
- According to the problem, the temperature in Miami is given as 82 degrees.
- Therefore, we can set up the equation for the temperature in Miami as 82 degrees equaling three times the temperature in Bangor plus 22 degrees.
- The equation for this relationship is:
[tex]\[
3x + 22 = 82
\][/tex]
4. Solve the Equation:
- We need to solve for `x` to find the temperature in Bangor.
- Start by subtracting 22 from both sides of the equation:
[tex]\[
3x + 22 - 22 = 82 - 22
\][/tex]
[tex]\[
3x = 60
\][/tex]
- Next, divide both sides by 3 to solve for `x`:
[tex]\[
x = \frac{60}{3}
\][/tex]
[tex]\[
x = 20
\][/tex]
5. Correct Choice:
- The correct form that represents the given problem is:
[tex]\[
3x - 82 = 22
\][/tex]
Thus, the equation is [tex]\(3x - 82 = 22\)[/tex], which correctly demonstrates that the temperature in Miami is 82 degrees, given the relationship described.
1. Define Variables:
- Let's let `x` represent the temperature in Bangor, Maine.
2. Understand the Relationship:
- The temperature in Miami is described as being 22 degrees warmer than three times the temperature in Bangor.
3. Write the Equation:
- According to the problem, the temperature in Miami is given as 82 degrees.
- Therefore, we can set up the equation for the temperature in Miami as 82 degrees equaling three times the temperature in Bangor plus 22 degrees.
- The equation for this relationship is:
[tex]\[
3x + 22 = 82
\][/tex]
4. Solve the Equation:
- We need to solve for `x` to find the temperature in Bangor.
- Start by subtracting 22 from both sides of the equation:
[tex]\[
3x + 22 - 22 = 82 - 22
\][/tex]
[tex]\[
3x = 60
\][/tex]
- Next, divide both sides by 3 to solve for `x`:
[tex]\[
x = \frac{60}{3}
\][/tex]
[tex]\[
x = 20
\][/tex]
5. Correct Choice:
- The correct form that represents the given problem is:
[tex]\[
3x - 82 = 22
\][/tex]
Thus, the equation is [tex]\(3x - 82 = 22\)[/tex], which correctly demonstrates that the temperature in Miami is 82 degrees, given the relationship described.
