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

none
none

3
3

1
1

2

Answer 1

To determine the number of equations that have the same solution set, we'll need to solve each equation.

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

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

Bringing like terms together:
\[ 135f - 100f = 315 - 200 \]
\[ 35f = 115 \]
\[ f = \frac{115}{35} = \frac{23}{7} \]

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

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

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

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

Rearranging the equation:
\[ 4h - 3h = -3 + 8 \]
\[ h = 5 \]

Now, we have the solutions for each equation:
- Equation A: \( f = \frac{23}{7} \)
- Equation B: \( g = \frac{81}{59} \)
- Equation C: \( h = 5 \)

Since each equation has a different solution set, the number of equations that share the same solution set is **none**.

Final response: **none**.