Yesterday, jack drove 40 1/2 miles. he used 1 1/4 gallons of gasoline. what is the unit rate for miles per gallons

From the information we have, Jack drove 401/2 miles and used a total of 1 1/4 gallons of gasoline.

We need to find out how many miles he travelled  per each gallon.

40 1/2 miles can be written as 40.5 miles

1 1/4 gallons  can be written as 1.25 gallons.

So now we form an equation.

40.5 = 1.25

   x = 1

Where x is the number of miles per gallon

We cross multiply the equation

40.5 * 1 = 1.25 * x

40.5 = 1.25x

40.5 / 1.25  = x

 32.4 = x

x = 32 .4

So the unit rate for miles per gallons is 32.4 miles per gallon

40 minutes

step-by-step explanation:

add the time and multiply by 2

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.