Which of the following pairs of equations has exactly the same solution?

Question

A. x/3.2 =1.8 and 1.8 x=3.2
B. 3/8x=1 and1/3x=1/8
C. -3.2x=0.64 and x/4= -0.05
D. -3/4x=5/2 and 5/2x= -3/4

Answer 1

To find the pair of equations that have the same solution, we can solve each pair of equations to see if they lead to the same value of x.

A. x/3.2 =1.8 and 1.8 x=3.2

For equation 1:
Multiply both sides by 3.2: x = 1.8 * 3.2 = 5.76

For equation 2:
Divide both sides by 1.8: x = 3.2/1.8 ≈ 1.778

These two equations do not have exactly the same solution.

B. 3/8x=1 and 1/3x=1/8

For equation 1:
Multiply both sides by 8/3: x = 8/3

For equation 2:
Multiply both sides by 3: x = 3/8

These two equations do not have exactly the same solution.

C. -3.2x=0.64 and x/4= -0.05

For equation 1:
Divide both sides by -3.2: x = 0.64 / -3.2 = -0.2

For equation 2:
Multiply both sides by 4: x = -0.05 * 4 = -0.2

These two equations have the same solution.

D. -3/4x=5/2 and 5/2x= -3/4

For equation 1:
Divide both sides by -3/4: x = (5/2) / (-3/4) = (-5/2) * (4/3) = -10/3

For equation 2:
Divide both sides by 5/2: x = (-3/4) / (5/2) = (-3/4) * (2/5) = -3/10

These two equations do not have exactly the same solution.

Therefore, the correct answer is C. -3.2x=0.64 and x/4= -0.05.