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

2
2 - no response given

3
3 - no response given

none
none - incorrect

1

1 answer

Let's solve each equation to identify their solution sets.

Equation A: \[ \frac{4}{5}(3f - 7) = \frac{2}{5}(4f - 8) \] Multiply both sides by 5 to eliminate the fractions: \[ 4(3f - 7) = 2(4f - 8) \] Distributing both sides: \[ 12f - 28 = 8f - 16 \] Rearranging to isolate \(f\): \[ 12f - 8f = -16 + 28 \] \[ 4f = 12 \] \[ f = 3 \]

Equation B: \[ \frac{5}{9}g - 2 = \frac{7}{9} \] Add 2 to both sides: \[ \frac{5}{9}g = \frac{7}{9} + 2 \] Convert 2 to a fraction with a denominator of 9, which is \(\frac{18}{9}\): \[ \frac{5}{9}g = \frac{25}{9} \] Multiply both sides by \(\frac{9}{5}\): \[ g = 5 \]

Equation C: \[ -2(4 - 2h) = -3(1 - h) \] Distributing both sides: \[ -8 + 4h = -3 + 3h \] Rearranging to isolate \(h\): \[ 4h - 3h = -3 + 8 \] \[ h = 5 \]

Now, we summarize the solutions:

  • Equation A has \(f = 3\)
  • Equation B has \(g = 5\)
  • Equation C has \(h = 5\)

From this analysis, the solution sets are:

  • A has a solution of 3.
  • B has a solution of 5.
  • C has a solution of 5.

Equations B and C have the same solution (5), which means there are 2 equations that share the same solution set.

The final answer is: 2