Question 3

The ratio of x to y to z is 4 to -3 to 5.

To determine the ratio of x to y to z, we can solve the equations given. By rearranging the equations appropriately, we find that the values lead us to the ratio of 4 for x, -3 for y, and 5 for z.

A) 3 to 4 to 5

This option is incorrect because substituting these values into the original equations does not satisfy both equations. The coefficients do not maintain the balance required by the relationships outlined in the problem.

B) 4 to 3 to 5

This option is also incorrect as it fails to hold true when applied to the original equations. The resulting values do not correspond to the derived equations, indicating a mismatch in the required ratio.

C) 4 to -3 to 5

This option is correct. After solving the equations, we find that x corresponds to 4, y corresponds to -3, and z corresponds to 5, satisfying the conditions set by the equations given in the problem.

D) 4 to 5 to 3

This option is incorrect as substituting these values into the original equations does not yield a true statement. The relationships established do not correspond with this ratio.

E) 5 to -3 to 4

This option is incorrect as well. When substituting these values back into the original equations, they do not satisfy the conditions laid out, demonstrating that this ratio is not valid.

Conclusion

The correct ratio of x to y to z is definitively 4 to -3 to 5, as it satisfies the equations provided. All other options fail to maintain the necessary balance required by the relationships in the problem, confirming that they cannot be correct. Thus, option C is the only valid answer.