Find the unknown value in the proportion [tex]x / 32=38 / 64[/tex].
A) 38
B) 19
C) 76
D) 54
Answer (2)
We have the proportion 32 x = 64 38 .
Multiply both sides by 32 to isolate x : x = 64 38 × 32 .
Simplify the expression: x = 2 38 .
Calculate the value of x : x = 19 . The answer is 19 .
Explanation
Understanding the Problem We are given the proportion 32 x = 64 38 and we need to find the value of x .
Isolating x To solve for x , we can multiply both sides of the equation by 32: 32 x × 32 = 64 38 × 32 This simplifies to: x = 64 38 × 32
Simplifying the Fraction Now, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. Notice that 32 divides both 32 and 64. So, we can simplify the fraction as follows: x = 64 38 × 32 = 2 38 × 1 = 2 38
Finding the Value of x Finally, we divide 38 by 2 to find the value of x : x = 2 38 = 19 So, the unknown value x is 19.
Examples
Proportions are useful in everyday life. For example, if you know that 2 apples cost 1 , 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 6 a ppl escos t . I n t hi sc a se , yo u w o u l d se t u pt h e p ro p or t i o na s \frac{2}{1} = \frac{6}{x} , w h ere x i s t h ecos t o f 6 a ppl es . S o l v in g f or x g i v esyo u x = 3$, so 6 apples cost $3. Proportions are also used in cooking, baking, and many other areas.
The unknown value x in the proportion 32 x = 64 38 is 19. We found this by simplifying the equation and isolating x . Therefore, the correct answer is option B) 19.
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