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 filling out the table showing how far she can travel for each gallon of gas that she uses. Find the missing values using the constant of proportionality of 28 miles per gallon.

a =
b =
c =

Answer 1

To solve the problem, we need to use the constant of proportionality, which is 28 miles per gallon. This means that for every gallon of gas used, Alexa can travel 28 miles.

We can fill in the missing values in the table based on this relationship.

1. For b (Gallons = b, miles = a):

   • We know that miles = gallons × 28.
   • For the second row, where gallons = b, we can express miles as: \[ a = b \times 28 \]

2. For a (Gallons = 4, miles = a):

   • Substitute 4 for gallons: \[ a = 4 \times 28 = 112 \]

3. For c (Gallons = 10, miles = c):

   • Substitute 10 for gallons: \[ c = 10 \times 28 = 280 \]

4. For b (Gallons = 2, miles = b):

   • Substitute 2 for gallons: \[ b = 2 \times 28 = 56 \]

So the final values are:

• a = 112
• b = 56
• c = 280

Thus, the missing values are:

• a = 112
• b = 56
• c = 280