# Thread: elimination and substitution question |:

1. ## elimination and substitution question |:

Hi guys , i am in grade 10 gifted math and am doing a series of word problems that involve elimination and substitution. I am good at math , but am still a bit ESL , so am having trouble decoding the first 2 equations that i am supposed to have.

The question is : A car averages 8.5L/100km in city driving and 6.3L/100km on the highway. In 720km of driving , it used 55.7L of fuel.
a)How far was the car driven in the city?
b)How much fuel did it use in city driving?

From what i read i figured that i would let the distance driven in the city be c km , and the distance driven in the highway be h km

The first equation in my opinion should be
c+h=720

I am unsure however on what the second equation should be.

I tried 8.5c+6.3H=720(55.7)

and my end-result of c , was over 1900. Obviously i made a mistake there x(.
i was thinking of doing it as 8.5c/100+ 6.3h/100= 720(55.7)/100 but this would simply give me the same wrong answer.

Any help would be much appreciated

2. Hello, mathdumby!

A car averages 8.5 L/100km in city driving and 6.3 L/100km on the highway.
In 720 km of driving , it used 55.7 L of fuel.

a) How far was the car driven in the city?
b) How much fuel did it use in city driving?

i figured that i would let the distance driven in the city be $\displaystyle c$ km,
and the distance driven in the highway be $\displaystyle h$ km

The first equation, in my opinion, should be: .$\displaystyle {\color{blue}c+h\:=\:720}$ . . . . Right!
I had to baby-talk my way through this . . .

In the city, the car uses 8.5 liters for 100 km of driving.
. . That is: .$\displaystyle \frac{8.5}{100} = 0.085$ liters per kilometer.
For $\displaystyle c$ km, it used: .$\displaystyle c \times 0.085 \:=\:0.085c$ liters of fuel.

On the highway, the car uses 6.3 liters for 100 km of driving.
. . That is: .$\displaystyle \frac{6.3}{100} = 0.063$ liters per kilometer.
For $\displaystyle h$ km, it used: .$\displaystyle h \times 0.063 \:=\:0.063h$ liters of fuel.

It used a total of 55.7 liters of fuel: .$\displaystyle {\color{blue}0.085c + 0.063h \:=\:55.7}$ . . . . There!

(I got: .$\displaystyle c = 470,\;h = 250$)

3. Thanks soroban xD I can't believe i didnt think of that. Your help is much appreciated