Question

Amy is buying a new car and wants to determine the gas mileage. The relationship between the gallons of gas, x, and the mileage, y, is proportional. The sticker on the car says the vehicle can travel 167.2 miles using 8 4/5 gallons of gas.

Which of the statements are true?

a. The car uses 19 gallons of gas for every 1 mile traveled.
b. The car can travel 19 miles for every 1 gallon of gas.
c. A coordinate that lies on the graph is (11.5,207).
d. The constant of proportionality is 19.
e. In order to determine the constant or proportionality, divide the miles by the gallons.
f. The constant of proportionality can be represented by the coordinate (1,19).
g. The constant of proportionality can be represented by the coordinate (19,1).

Answer 1

The true statements regarding the constant of proportionality are: true statements are b, d, e, and f.

How to find the constant of proportionality?

Given: The car can travel 167.2 miles using 8 4/5 gallons of gas.

Let's first find the mileage per gallon:

`\[ \text{Mileage per gallon} = \frac{\text{Total miles}}{\text{Gallons of gas}} \]`

`\[ \text{Mileage per gallon} = (167.2)/(8 (4)/(5)) \]`

To simplify, convert the mixed number to an improper fraction:

`\[ \text{Mileage per gallon} = (167.2)/((44)/(5)) \]`

Now, invert and multiply to find the mileage per gallon:

`\[ \text{Mileage per gallon} = 167.2 * (5)/(44) \]`

`\[ \text{Mileage per gallon} = (167.2 * 5)/(44) \]`

`\[ \text{Mileage per gallon} = (836)/(44) \]`

Mileage per gallon} = 19

So, the car can travel 19 miles for every 1 gallon of gas.

Now, let's evaluate each statement:

a. Statement A is false because the correct relationship is that the car travels 19 miles for every 1 gallon of gas.

b. The statement "the car can travel 19 miles for every 1 gallon of gas" is TRUE as determined above.

c. The coordinate (11.5, 207) does not lie on the graph because 207/11.5 = 18 instead of 19.

d. The constant of proportionality is 19 because, as we have solved above, mileage per gallon = 19.

e. In order to determine the constant of proportionality we have to divide the miles by the gallons because that's how to find the constant of proportionality.

f. The constant of proportionality can be represented by the coordinate (1,19) because it represents the relationship between 1 gallon of gas and 19 miles.

g. The constant of proportionality cannot be represented by the coordinate (19,1) because the correct representation is (1, 19), as the constant of proportionality is the mileage per gallon.

Therefore, the true statements are b, d, e, and f.