Find the unknown value in the proportion [tex]9 / x=27 / 39[/tex].
A) 13
B) 36
C) 38
D) 6.2
Answer (2)
Cross-multiply the proportion: 9 \t \t × 39 = 27 × x .
Simplify the equation: 351 = 27 x .
Divide both sides by 27 to isolate x : x = 27 351 .
Calculate the value of x : 13 .
Explanation
Understanding the Proportion We are given the proportion x 9 = 39 27 . Our goal is to find the value of x that makes this proportion true.
Cross-Multiplication To solve for x , we can cross-multiply. This means we multiply the numerator of the first fraction by the denominator of the second fraction, and set it equal to the product of the denominator of the first fraction and the numerator of the second fraction: 9 × 39 = 27 × x
Simplifying the Equation Now, we perform the multiplication: 351 = 27 x
Isolating x To isolate x , we divide both sides of the equation by 27: x = 27 351
Calculating x Now we perform the division to find the value of x : x = 13
Final Answer Therefore, the unknown value in the proportion is 13.
Examples
Proportions are useful in everyday life. For example, if you know that 3 apples cost 2 , yo u c an u se a p ro p or t i o n t o f in d o u t h o w m u c h 15 a ppl es w o u l d cos t . S e tt in gu pt h e p ro p or t i o n \frac{3}{2} = \frac{15}{x} , yo u c an so l v e f or x$ to find the cost of 15 apples. This concept is also used in scaling recipes, converting units, and calculating discounts.
The unknown value in the proportion x 9 = 39 27 is 13 . This is found by cross-multiplying, simplifying, and isolating x . Therefore, the correct answer is option A) 13.
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