Julio has found that his new car gets 36 miles to the gallon on the highway and 31 miles per gallon in the city. he recently drove 397 miles on 12 gallons of gasoline. how many miles did he drive on the highway? how many miles did he drive in the city?

Miles he drove on highway = 180 miles

Miles he drove in the city = 217 miles

Step-by-step explanation:

Lets assume that gallon used on highway = x

Miles driven on highway = y

(I) 36 miles per gallon on the highway.

36x = y    equation 1

(II) 31 miles per gallon in the city.He recently drove 397 miles on 12 gallons of gasoline

31(12-x)= 397-y    equation 2

372-31x= 397-y

Combine the constants:

-31x= 397-372-y

y-31x = 25

Now substitute the value of equation 1 in equation 2

y-31x=25

36x-31x=25

5x=25

Now divide both sides by 5

5x/5=25/5

x=5

Now substitute the value x=5 in equation 1

36x=y

36(5)=y

180= y

Now subtract the miles driven on highway from recently drove miles to get the miles driven in the city.

397-y = 389 - 180

= 217

Therefore,

Miles he drove on highway = 180 miles

Miles he drove in the city = 217 miles

picture below

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15