To find the unknown value [tex]\( x \)[/tex] using proportional reasoning, we need to understand the relationship between the miles traveled and the gallons of gas used. The table provided shows that for every 1 gallon of gas used, a car can travel 30.5 miles. We can generalize this to say that:
[tex]\[ \text{Miles Traveled} = \text{Miles per Gallon} \times \text{Gallons of Gas Used} \][/tex]
Given:
- The car travels 30.5 miles for every gallon of gas.
- We need to find the number of miles traveled ([tex]\( x \)[/tex]) when 3 gallons of gas are used.
Let's use the formula to find [tex]\( x \)[/tex]:
[tex]\[ x = \text{Miles per Gallon} \times \text{Gallons of Gas Used} \][/tex]
Substitute the known values into the formula:
[tex]\[ x = 30.5 \, \text{miles/gallon} \times 3 \, \text{gallons} \][/tex]
By performing the multiplication, we find:
[tex]\[ x = 91.5 \, \text{miles} \][/tex]
Thus, the value of [tex]\( x \)[/tex] that completes the table is:
[tex]\[ x = 91.5 \][/tex]
So, when 3 gallons of gas are used, the car travels 91.5 miles.
