Ratio and Proportion: 0.6: X:: 7:42
A.
X=2.4
B.
X=0.6
C.
X=1.2
D.
X=3.6
The Correct answer and Explanation is:
To solve the ratio and proportion problem 0.6:X::7:420.6:X::7:420.6:X::7:42, we need to find the value of XXX that maintains the equality between the two ratios. This problem can be approached by setting up a proportion and solving for XXX.
Step-by-Step Solution:
- Set Up the Proportion:The ratio 0.6:X0.6:X0.6:X is equivalent to the ratio 7:427:427:42. We can write this as:0.6X=742\frac{0.6}{X} = \frac{7}{42}X0.6=427
- Solve the Proportion:To solve for XXX, we need to cross-multiply and then isolate XXX. Cross-multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction:0.6×42=7×X0.6 \times 42 = 7 \times X0.6×42=7×X
- Perform the Multiplication:Calculate 0.6×420.6 \times 420.6×42:0.6×42=25.20.6 \times 42 = 25.20.6×42=25.2Thus, we have:25.2=7×X25.2 = 7 \times X25.2=7×X
- Isolate XXX:To find XXX, divide both sides of the equation by 7:X=25.27X = \frac{25.2}{7}X=725.2
- Perform the Division:Calculate 25.27\frac{25.2}{7}725.2:25.27=3.6\frac{25.2}{7} = 3.6725.2=3.6Thus, X=3.6X = 3.6X=3.6.
Conclusion:
The correct answer is X=3.6X = 3.6X=3.6. This result is found by maintaining the equality of the two ratios through cross-multiplying and solving the resulting equation. This method is a standard approach for solving proportion problems, ensuring that the ratios remain equivalent when the unknown variable is determined.
Answer: D. X=3.6X = 3.6X=3.6