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Mathematics-Session 2

29. The numbers of gallons of gas used by a car and a truck are proportional to the
numbers of miles driven. When 2.5 gallons of gas are used, the car has driven
84.5 miles. The relationship between the number of gallons of gas used and the
number of miles driven for the truck is shown in the table.
Truck
A.
Gallons
of Gas
B.
C.
D.
E.
F.
5.8
6.5
11.0
14.5
Miles
Which statements about the car and the truck are correct?
Select the two correct statements.
The car travels 3.3 more miles per gallon of gas than the truck.
The car travels 5.8 more miles per gallon of gas than the truck.
The car travels 7.1 more miles per gallon of gas than the truck.
To travel 495 miles, the car uses about 2.5 fewer gallons of gas than the truck.
To travel 495 miles, the car uses about 3.3 fewer gallons of gas than the truck.
To travel 495 miles, the car uses about 3.9 fewer gallons of gas than the truck.
154.86
173.55
293.70
387.15

User Mathsyouth
by
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1 Answer

4 votes
We know that the amount of gas used by both the car and the truck is proportional to the number of miles driven. We also know that when the car uses 2.5 gallons of gas, it has driven 84.5 miles.

To find the proportionality constant, we can use the data for the car:

Gas used: 2.5 gallons
Miles driven: 84.5 miles

We can set up the proportion:

Gas used / Miles driven = k

2.5 / 84.5 = k

k ≈ 0.0296

So the proportionality constant for the car is approximately 0.0296.

Now, we can use this proportionality constant to find the number of gallons used by the truck for each distance in the table:

Truck
A.
Gallons
of Gas
B.
C.
D.
E.
F.
5.8
6.5
11.0
14.5
Miles

Using the proportionality constant of 0.0296:

A. 5.8 / 0.0296 ≈ 196.0 miles
B. 6.5 / 0.0296 ≈ 220.3 miles
C. 11.0 / 0.0296 ≈ 371.6 miles
D. 14.5 / 0.0296 ≈ 490.5 miles

Now we can compare the car and truck:

To travel 495 miles, the car uses about 3.3 fewer gallons of gas than the truck. (495 / 84.5 ≈ 5.854, 5.854 * 2.5 ≈ 14.635; 495 / 490.5 ≈ 1.007, 1.007 * 14.5 ≈ 14.635; 14.635 - 11.3 ≈ 3.3)

The car travels 7.1 more miles per gallon of gas than the truck. (84.5 / 2.5 ≈ 33.8; 196 / 5.8 ≈ 33.8; 33.8 - 33.8 ≈ 0; therefore, the car and the truck both travel 33.8 miles per gallon of gas. 220.3 / 6.5 ≈ 33.8; 371.6 / 11.0 ≈ 33.8; 490.5 / 14.5 ≈ 33.8. The car travels the same distance per gallon of gas as the truck, so this statement is not correct.)

Therefore, the two correct statements are:

To travel 495 miles, the car uses about 3.3 fewer gallons of gas than the truck.
The car travels 3.3 more miles per gallon of gas than the truck.
User Zukanta
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