What is the missing value for gallons and miles in the table?
Understand the Problem
The question is asking to fill in the missing values in a table that relates gallons of fuel to miles driven. This involves calculating the mileage per gallon based on the provided values.
Answer
The missing values are $1$ gallon and $225$ miles.
Answer for screen readers
The missing values in the table are:
- For Gallons in the first row: $1$
- For Miles in the last row: $225$
Steps to Solve
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Determine mileage for 4 gallons To find the miles per gallon for 4 gallons, use the formula: $$ \text{Mileage} = \frac{\text{Miles}}{\text{Gallons}} $$ Substituting in the values: $$ \text{Mileage} = \frac{180}{4} = 45 \text{ miles per gallon} $$
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Calculate the missing gallons for 45 miles Using the formula again for 45 miles: $$ \text{Gallons} = \frac{\text{Miles}}{\text{Mileage}} $$ Assuming the same mileage of 45 miles per gallon: $$ \text{Gallons} = \frac{45}{45} = 1 \text{ gallon} $$
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Determine the miles for 5 gallons using known mileage Now we can find the miles for 5 gallons using the same mileage of 45 miles per gallon: $$ \text{Miles} = \text{Gallons} \times \text{Mileage} $$ Substituting in the values: $$ \text{Miles} = 5 \times 45 = 225 \text{ miles} $$
The missing values in the table are:
- For Gallons in the first row: $1$
- For Miles in the last row: $225$
More Information
In this table, the miles driven per gallon is consistently used, allowing for straightforward calculations using the formula for mileage. Keeping the mileage constant simplifies finding the unknowns.
Tips
- Mistaking the mileage as a variable instead of a constant; remember it stays the same unless specified otherwise.
- Not using the same units when performing calculations; check that both miles and gallons are consistently used.
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