34. 20:5 = 30:x. Find the value of x. (Enter the numerical value only. Round to the nearest tenth.)
Answer: C
x = 7.5
To solve the proportion 20:5 = 30:x, we can use cross-multiplication. This leads us to the equation 20x = 150, from which we can determine that x equals 7.5.
A) 5
Option A is incorrect because substituting x with 5 in the equation results in 20:5 = 30:5, which simplifies to 4 = 6, a false statement. This does not satisfy the original proportion.
B) 6
Option B is also incorrect. If we substitute x with 6, the equation becomes 20:5 = 30:6, simplifying to 4 = 5, which is not true. Therefore, it does not represent a valid solution to the proportion.
C) 7.5
Option C is correct. When we substitute x with 7.5, the equation 20:5 = 30:7.5 simplifies to 4 = 4, confirming that this satisfies the original proportion accurately.
D) 8
Option D is incorrect because substituting x with 8 results in 20:5 = 30:8, which simplifies to 4 = 3.75, a false statement. Thus, it does not fulfill the requirements of the proportion.
Conclusion
The correct answer is 7.5, as it maintains the equality in the original proportion when calculated. Options A, B, and D do not satisfy the mathematical relationship established in the equation, making them invalid solutions. Only option C accurately reflects the correct value of x.