Let's find out how many inches taller Tonya is than Mary by examining each equation step-by-step.
### Examining Each Equation:
1. Equation: [tex]\( x + 70 = 63.5 \)[/tex]
- Subtract 70 from both sides:
[tex]\[
x + 70 - 70 = 63.5 - 70
\][/tex]
[tex]\[
x = -6.5
\][/tex]
- The answer here is [tex]\(-6.5\)[/tex] inches, which does not make sense in the context of this problem.
2. Equation: [tex]\( 63.5 + x = 70 \)[/tex]
- Subtract 63.5 from both sides:
[tex]\[
63.5 + x - 63.5 = 70 - 63.5
\][/tex]
[tex]\[
x = 6.5
\][/tex]
- The answer here is [tex]\(6.5\)[/tex] inches, which makes sense. Tonya is 6.5 inches taller than Mary.
3. Equation: [tex]\( x - 63.5 = 70 \)[/tex]
- Add 63.5 to the left side and subtract 63.5 from the right side:
[tex]\[
x - 63.5 + 63.5 = 70 + 63.5
\][/tex]
[tex]\[
x = 133.5
\][/tex]
- The answer here is [tex]\(133.5\)[/tex] inches, which does not make sense in the context of this problem.
4. Equation: [tex]\( 63.5 - x = 70 \)[/tex]
- Subtract 63.5 from both sides:
[tex]\[
63.5 - x - 63.5 = 70 - 63.5
\][/tex]
[tex]\[
-x = 6.5
\][/tex]
- Then, multiply both sides by [tex]\(-1\)[/tex]:
[tex]\[
x = -6.5
\][/tex]
- The answer here is [tex]\(-6.5\)[/tex] inches, which does not make sense in the context of this problem.
### Conclusion:
From the equations, the correct and logical solution comes from the equation [tex]\(63.5 + x = 70\)[/tex]. Subtracting 63.5 from both sides confirms that:
[tex]\[
x = 6.5
\][/tex]
Therefore, Tonya is 6.5 inches taller than Mary.
