A 2-column table with 4 rows. Column 1 is labeled Gallons with entries 2, 4, b, 10. Column 2 is labeled miles with entries 56, a, 168, c.

Question

Alexa is planning to drive across the United States in her car. She started making a table to represent the proportional relationship between gallons of gas and miles driven. The table shows how far she can travel for each gallon of gas that she uses.

What is the constant of proportionality?
miles per gallon

Answer 1

To find the constant of proportionality (miles per gallon), we need to calculate the ratio of miles to gallons for each of the rows where we have complete entries. The constant of proportionality should be the same across all these ratios if they are indeed proportional.

Given the table:

| Gallons | Miles | |---------|-------| | 2 | 56 | | 4 | a | | b | 168 | | 10 | c |

We'll calculate the ratios for the complete rows, starting with the first row (2 gallons and 56 miles):

1. For 2 gallons: \[ \text{Constant of proportionality} = \frac{\text{Miles}}{\text{Gallons}} = \frac{56}{2} = 28 \text{ miles per gallon} \]

Next, we can use this constant to find the values of \(a\), \(b\), and \(c\) as follows:

2. For 4 gallons (to find \(a\)): \[ a = 4 \times 28 = 112 \text{ miles} \]

3. For \(b\) gallons (given 168 miles): \[ b = \frac{168}{28} = 6 \text{ gallons} \]

4. For 10 gallons (to find \(c\)): \[ c = 10 \times 28 = 280 \text{ miles} \]

Now, we can rewrite the complete table:

| Gallons | Miles | |---------|-------| | 2 | 56 | | 4 | 112 | | 6 | 168 | | 10 | 280 |

Thus, the constant of proportionality is 28 miles per gallon.