We want to find how many miles a particular car can travel after a low fuel warning appears. To do so, we will first rewrite the given repeating decimal as a fraction to find out how much fuel is left in the car. Let's recall how to write a repeating decimal as a fraction.
Write the equation x=d, where d is a repeating decimal.
Subtract the equation from the previous step from the equation 10^n x=10^n d, where n is the number of repeating digits.
Solve the equation for x.
We can use this process to rewrite 0.0146 as a fraction. We will substitute 0.0146 for d and 1 for n, as there is only one repeating digit in the decimal.
ccc x=d & ⇔ & x= 0.0146 10^nx=10^n d & ⇔ & 10^1x=10^1( 0.0146)
Let's simplify the second equation.
10^1x=10^1(0.0146) ⇒ 10x=0.146
Now we are ready to subtract the first equation from the second one.
c r c l& 10x & = & 0.146 -( & x & = & 0.0146 ) & 9x & = & 0.132
Finally, we can solve for x. Let's do it!
The car has 1329000 of a tank of gas remaining. From the exercise, we know that the tank holds 18.5 gallons of gas. We can find out how much gas is left in the tank if we multiply 18.5 by 1329000. Let's do it.
18.5* 132/9000=2442/9000
Next, we know that the car can travel 36 miles for each gallon of gas used. We can create a proportion that models this situation using y to represent the distance the car can travel with 24429000 of a tank of gas remaining.
36miles/1gallon=ymiles/24429000gallon
Let's cross multiply this proportion to find the value of y. For simplicity, we will ignore the units for our calculations.
