To determine the value that makes the given numbers proportional, we can set up the proportion equation and solve for the unknown variable. Let's denote this unknown value by [tex]\( x \)[/tex].
Given:
[tex]\[ \frac{25.4}{x} = \frac{9}{13.5} \][/tex]
Now, we solve for [tex]\( x \)[/tex]:
1. Cross-multiply to get rid of the fraction:
[tex]\[ 25.4 \times 13.5 = 9 \times x \][/tex]
2. Simplify the multiplication on the left side:
[tex]\[ 342.9 = 9x \][/tex]
3. Isolate [tex]\( x \)[/tex] by dividing both sides by 9:
[tex]\[ x = \frac{342.9}{9} \][/tex]
4. Perform the division:
[tex]\[ x = 38.1 \div 9 = 4.783464566929134 \approx 4.78 \][/tex]
Since we have the options 6, 8, and 9, and our calculated value [tex]\(\approx 4.78\)[/tex] does not match any of the options provided, it appears there may be a misunderstanding in the problem's multiple-choice answers. Nonetheless, based on the calculated answer, none of the given options (6, 8, 9) are correct.
