Complete the ratio table.
Understand the Problem
The question is asking to complete the given ratio table by determining the missing values based on the existing ratios provided. The ratios seem to be related to a specific linear relationship that needs to be identified.
Answer
The missing values are $672$ and approximately $45$.
Answer for screen readers
The missing values in the ratio table are:
- For 501, the value is $672$.
- For 835, the value is approximately $45$.
Steps to Solve
- Identify the Ratio Relationship
First, look at the ratios given in the table. The first column values (167, 334, 501, 835) seem to be increasing linearly, while the second column values (9, 18, 27, 36) also follow a linear pattern. We need to determine the relationship between the two columns.
- Find the Pattern in the Second Column
Notice the second column increments by 9:
- From 9 to 18, the increase is 9.
- From 18 to 27, the increase is also 9.
- From 27 to 36, again, the increase is 9.
This suggests that the second column, $y$, can be expressed as:
$$ y = \frac{x}{18.67} $$
where $x$ is the first column value.
- Calculate the Missing Value in the First Column
Now, we need to find the relationship for the missing value in the first column, which corresponds to 36 in the second column. Using the derived equation:
$$ 36 = \frac{x}{18.67} $$
To find $x$, we solve the equation:
$$ x = 36 \times 18.67 $$
Calculating this gives:
$$ x = 672.12 $$
- Find the Ratio for 835
Next, we'll calculate the missing second column value for the first column value 835:
Using the equation we derived earlier:
$$ y = \frac{835}{18.67} $$
Calculating this gives:
$$ y \approx 44.8 $$
The missing values in the ratio table are:
- For 501, the value is $672$.
- For 835, the value is approximately $45$.
More Information
The calculations show how the ratios are linearly related. Each number in the second column corresponds to the first column divided by approximately 18.67. The patterns illustrate proportional relationships often found in ratio problems.
Tips
- Confusing the relationship between the ratios. It's crucial to determine if they increase linearly or follow another pattern.
- Miscalculating the multiplication or division, which can lead to incorrect missing value estimates.
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