The problem asks to select all ratios that are equivalent to the ratio $16:14$. The available options are $64:56$, $24:21$, and $104:98$.

1. Problem Description

The problem asks to select all ratios that are equivalent to the ratio $16:14$. The available options are $64:56$, $24:21$, and $104:98$.

2. Solution Steps

First, simplify the given ratio $16:14$ by dividing both sides by their greatest common divisor, which is 2:

$16:14 = (16/2):(14/2) = 8:7$.

Now, check each of the given options to see if they are equivalent to $8:7$.

* Option 1: $64:56$

Divide both sides by 8:

$64:56 = (64/8):(56/8) = 8:7$.

So, $64:56$ is equivalent to $16:14$.

* Option 2: $24:21$

Divide both sides by 3:

$24:21 = (24/3):(21/3) = 8:7$.

So, $24:21$ is equivalent to $16:14$.

* Option 3: $104:98$

Divide both sides by 2:

$104:98 = (104/2):(98/2) = 52:49$.

Check if this is equivalent to $8:7$ by checking if $\frac{52}{8} = \frac{49}{7}$.

$\frac{52}{8} = \frac{13}{2}$ and $\frac{49}{7} = 7$.

Since $\frac{13}{2} \ne 7$, the ratio $104:98$ is not equivalent to $8:7$, and therefore not equivalent to $16:14$.

Another way is to divide 104 and 98 by 13 and 14 respectively, which would yield $104/13 = 8$ and $98/14 = 7$. Hence $104:98=13(8):14(7)$. Since the original ratio $16:14=2(8):2(7)$ we get that these two are equal by multiplying by 13/2=6.

5. Let's check that:

$16(6.5)=104$ and $14(6.5)=91$. Hence the ratio of $104:98$ is not equivalent to $16:14$.

Therefore, the ratios equivalent to $16:14$ are $64:56$ and $24:21$.

3. Final Answer

The ratios equivalent to $16:14$ are $64:56$ and $24:21$.