Math question that involves setting up a system of equations

Question

Julio has found that his new car gets 36 miles per 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?

Answer 1

write a system of equation( use elimination method to solve)

 

(1) 36x+31y=397

(2)     x + y  =  12

 

2. create a third equation to make one of your variables the same so that you can eliminate it.

you may decide to multiply equation (2) by 36 or 31 to create your new equation.(your x or y variables must be equal in both equations) 36x+36y=(36•12) or31x+31y=(31•12)(work out the numbers)

 

3.  subtract one equation from the other (usually the smaller from the larger will make it easier)  this will give you only one variable.. either x only or y only depend on the equation (3) you choose to create...   ( remember to subtract all variables including the whole numbers.. ) you will end up with a simple equation.. solve for x or y...

 

4.  substitute your value in its corresponding place in the first equation... so if you solved for x then the value you get will replace the x in equation(1) ⇒ 36(value) + 31y = 397

one you have done that you will have a simple equation with one variable and you can work it out for the next value

 

use equation (2) to test your answers

 

now that you have these apply both to your original equation to find your miles.. so  36(x value)+ 31(y value)= 397mi

 

your answer should be correct to exact figures...  

all the best

 

 

 

 

Answer 2

h is the number of miles driven on the highway

c is the number of miles driven in the city

 

You have two variables, you will need a system of two equations to solve the problem.

 

To calculate gallons for each style of driving, divide miles traveled by the miles per gallon of the rate.

 

(h mi)/(36mpg) + (c mi)/(31mpg) = 12 gal

 

(h mi) + (c mi) = 397 mi

 

Solve one equation for one of the variables

h mi = (397 - c) mi

 

Substitute that value into the second equation

(397 - c)mi/36 mpg + (c mi)/(31mpg) = 12 gal

 

(397/36 - c/36 + c/31) gal = 12 gal

1.03 + c(67/1116) = 12

c (67/1116) = 10.97

c = 182.72

 

Now substitute that answer into the second equation

 

182.72mi + h mi = 397 mi

 

h = 214.28

 

Check your work by substituting both values back into the first equation

 

(214.28)/36 + (182.72)/31 = 12

5.95 + 5.89 = 12

11.84 = 12

 

11.82 does not equal 12, but the units given in the problem had two significant digits.  Since the answer cannot be more accurate than the information given, i.e. two significant digits, this answer, to two significant digits, is:

 

12 gal = 12 gal