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

Question

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 identify the number of equations that have the same solution set, we'll solve each equation for its variable and see if they yield the same solution.

Equation A:

$$45(3f-7)=25(4f-8)$$

Expanding both sides:

$$135f-315=100f-200$$

Rearranging:

$$135f-100f=315-200$$ $$35f=115$$ $$f=\frac{115}{35}=\frac{23}{7}$$

Equation B:

$$59g-2=79$$

Rearranging:

$$59g=79+2$$ $$59g=81$$ $$g=\frac{81}{59}$$

Equation C:

$$-2(4-2h)=-3(1-h)$$

Expanding both sides:

$$-8+4h=-3+3h$$

Rearranging:

$$4h-3h=-3+8$$ $$h=5$$

Summary of Solutions:

1. Equation A has the solution $f=\frac{23}{7}$.
2. Equation B has the solution $g=\frac{81}{59}$.
3. Equation C has the solution $h=5$.

All solutions are different.

Thus, the number of equations that have the same solution set is none.

Correct response: none