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  1. #1
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    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
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  2. #2
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    Lexington, MA (USA)
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    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 c km,
    and the distance driven in the highway be h km

    The first equation, in my opinion, should be: . {\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: . \frac{8.5}{100} = 0.085 liters per kilometer.
    For c km, it used: . 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: . \frac{6.3}{100} = 0.063 liters per kilometer.
    For h km, it used: . h \times 0.063 \:=\:0.063h liters of fuel.


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


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

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