Question

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

Equation A: 4/5(3f−7)=2/5(4f−8)

Equation B: 5/9g−2=7/9

Equation C: −2(4−2h)=−3(1−h)

(1 point)
Responses

none
none - incorrect

3
3 - no response given

2

Answer 1

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

**Equation A:**
\[
\frac{4}{5}(3f - 7) = \frac{2}{5}(4f - 8)
\]
First, let's eliminate the fractions by multiplying both sides by 5:
\[
4(3f - 7) = 2(4f - 8)
\]
Expanding both sides:
\[
12f - 28 = 8f - 16
\]
Rearranging gives:
\[
12f - 8f = -16 + 28
\]
\[
4f = 12
\]
\[
f = 3
\]

**Equation B:**
\[
\frac{5}{9}g - 2 = \frac{7}{9}
\]
Adding 2 to both sides:
\[
\frac{5}{9}g = \frac{7}{9} + 2
\]
To add 2, first convert it to a fraction:
\[
2 = \frac{18}{9}
\]
So,
\[
\frac{5}{9}g = \frac{7}{9} + \frac{18}{9} = \frac{25}{9}
\]
Multiplying both sides by \(\frac{9}{5}\):
\[
g = \frac{9}{5} \cdot \frac{25}{9} = 5
\]

**Equation C:**
\[
-2(4 - 2h) = -3(1 - h)
\]
Expanding:
\[
-8 + 4h = -3 + 3h
\]
Rearranging gives:
\[
4h - 3h = -3 + 8
\]
\[
h = 5
\]

Now, we summarize the solutions:
- Equation A has the solution \(f = 3\).
- Equation B has the solution \(g = 5\).
- Equation C has the solution \(h = 5\).

Since:
- Equation A has a solution of \(3\),
- Equation B and C both have a solution of \(5\).

Equations B and C have the same solution, but Equation A does not match with the others.

Thus, the number of equations that have the same solution set is **2** (Equations B and C).

The correct response is:
**2**.