High School

The ratios [tex]4:7[/tex] and [tex]16:x[/tex] are equivalent. Find [tex]x[/tex].

[tex]x =[/tex]

Which of the following ratios are not equivalent?

A. [tex]4:7[/tex] and [tex]16:28[/tex]
B. [tex]4:7[/tex] and [tex]8:14[/tex]
C. [tex]4:7[/tex] and [tex]12:21[/tex]
D. [tex]4:7[/tex] and [tex]16:30[/tex]

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]