Complete the ratio table.
Understand the Problem
The question is asking to complete a ratio table by finding the missing values in a pair of rows based on the established ratios of given numbers.
Answer
The missing values are \( x = 393 \) and \( y = 290 \).
Answer for screen readers
The completed ratio table is:
| 197 | 58 |
|---|---|
| 393 | 116 |
| 788 | 232 |
| 985 | 290 |
Steps to Solve
- Identify Known Ratios
The known ratios from the table are:
- ( \frac{197}{58} )
- ( \frac{116}{x} )
- ( \frac{788}{232} )
- ( \frac{290}{y} )
- Set Up Ratios for Missing Values
We will set up ratios to find the missing values in the table by using proportional relationships.
For the first row: $$ \frac{197}{58} = \frac{x}{116} $$
For the second row: $$ \frac{788}{232} = \frac{985}{290} $$
- Solve for the First Missing Value (x)
From the first ratio: $$ 197 \cdot 116 = 58 \cdot x $$
Calculating: $$ x = \frac{197 \cdot 116}{58} $$
- Calculate x
Perform the multiplication and division: $$ x = \frac{22852}{58} = 393 $$
- Solve for the Second Missing Value (y)
For the second row, we use: $$ \frac{788}{232} = \frac{985}{y} $$
Cross-multiply: $$ 788 \cdot y = 232 \cdot 985 $$
- Calculate y
Dividing gives us: $$ y = \frac{232 \cdot 985}{788} $$
- Final Calculation for y
Calculating: $$ y = \frac{228520}{788} = 290 $$
The completed ratio table is:
| 197 | 58 |
|---|---|
| 393 | 116 |
| 788 | 232 |
| 985 | 290 |
More Information
The ratios in each row maintain a consistent proportion, allowing us to deduce the missing values using cross multiplication.
Tips
- Forgetting to cross-multiply when setting up ratios.
- Using incorrect operations when calculating for the missing values.
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