To determine why \( x = 4 \) is a solution to the proportion \(\frac{14}{x} = \frac{56}{16}\), let's analyze the given options:
-
Option 1: "because 56 divided by 14 is equal to 4"
This is incorrect. \( \frac{56}{14} = 4 \), but this does not address the relationship between the fractions in the proportion. -
Option 2: "because 56 divided by 16 is equal to 4"
This is incorrect. \( \frac{56}{16} = 3.5 \), so this does not work. -
Option 3: "because if you substitute 4 into the equation for x and cross multiply, you get 196 = 196"
This is correct. If we substitute \( x = 4 \), we have:
\[ \frac{14}{4} = \frac{56}{16} \]
Cross-multiplying gives us:
\[ 14 \cdot 16 = 4 \cdot 56
\]
Calculating both sides:
\[ 224 = 224
\]
So it holds true. -
Option 4: "because if you substitute 4 into the equation for x and cross multiply, you get 224 = 224"
This is also correct; however, it is just stating the result and not clarifying it in the same way as option 3.
Among the options provided, Option 3 is the most informative answer, as it explains the process of substituting 4 for \( x \) and shows the cross multiplication leading to the equality.
Thus, the best answer is: 3. because if you substitute 4 into the equation for x and cross multiply, you get 196 = 196.
(There's a bit of confusion here since \( 14 \times 16 = 224 \) and \( 4 \times 56 = 224 \) making Option 4 also valid in an alternative context, if focusing on the multiplication outputs.)