Question

Identify the number of equations that have the same solution set.

Equation A: 45(3f−7)=25(4f−8)


Equation B: 59g−2=79


Equation C: −2(4−2h)=−3(1−h)


(1 point)
Responses

2
2

none
none

3
3

1

Answer 1

To determine how many of the given equations have the same solution set, we need to solve each equation and analyze their solutions.

**Equation A:**
\[ 45(3f - 7) = 25(4f - 8) \]

Expanding both sides:
\[ 135f - 315 = 100f - 200 \]

Rearranging gives us:
\[ 135f - 100f = 315 - 200 \]
\[ 35f = 115 \]
\[ f = \frac{115}{35} = \frac{23}{7} \]

So the solution for Equation A is \( f = \frac{23}{7} \).

**Equation B:**
\[ 59g - 2 = 79 \]

Adding 2 to both sides:
\[ 59g = 81 \]

Dividing by 59:
\[ g = \frac{81}{59} \]

So the solution for Equation B is \( g = \frac{81}{59} \).

**Equation C:**
\[ -2(4 - 2h) = -3(1 - h) \]

Distributing gives us:
\[ -8 + 4h = -3 + 3h \]

Rearranging gives us:
\[ 4h - 3h = -3 + 8 \]
\[ h = 5 \]

So the solution for Equation C is \( h = 5 \).

Now let's summarize the solutions:
- Equation A has \( f = \frac{23}{7} \)
- Equation B has \( g = \frac{81}{59} \)
- Equation C has \( h = 5 \)

Since all three equations have different solutions, they do not have the same solution set.

Thus, the final answer is:
**none**.