Answer :
To find the value of [tex]\( x \)[/tex] such that the ratios [tex]\( 4 : 7 \)[/tex] and [tex]\( 16 : x \)[/tex] are equivalent, we can follow these steps:
1. Write the ratios as fractions for comparison:
[tex]\[
\frac{4}{7} = \frac{16}{x}
\][/tex]
2. To solve for [tex]\( x \)[/tex], we need to cross-multiply. This means we multiply the numerator of the first fraction by the denominator of the second fraction and vice versa:
[tex]\[
4 \cdot x = 7 \cdot 16
\][/tex]
3. Next, we calculate the right side of the equation:
[tex]\[
4x = 112
\][/tex]
4. To isolate [tex]\( x \)[/tex], divide both sides of the equation by 4:
[tex]\[
x = \frac{112}{4}
\][/tex]
5. Perform the division:
[tex]\[
x = 28
\][/tex]
Hence, the value of [tex]\( x \)[/tex] is [tex]\( 28 \)[/tex].
So, the final answer is:
[tex]\[
x = 28
\][/tex]
1. Write the ratios as fractions for comparison:
[tex]\[
\frac{4}{7} = \frac{16}{x}
\][/tex]
2. To solve for [tex]\( x \)[/tex], we need to cross-multiply. This means we multiply the numerator of the first fraction by the denominator of the second fraction and vice versa:
[tex]\[
4 \cdot x = 7 \cdot 16
\][/tex]
3. Next, we calculate the right side of the equation:
[tex]\[
4x = 112
\][/tex]
4. To isolate [tex]\( x \)[/tex], divide both sides of the equation by 4:
[tex]\[
x = \frac{112}{4}
\][/tex]
5. Perform the division:
[tex]\[
x = 28
\][/tex]
Hence, the value of [tex]\( x \)[/tex] is [tex]\( 28 \)[/tex].
So, the final answer is:
[tex]\[
x = 28
\][/tex]
