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Math Help - Maths method 11 Linear equation problem solving

  1. #1
    Newbie fresh_'s Avatar
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    Maths method 11 Linear equation problem solving

    Hello I've received holiday homework from my text book and i cant seem to work ou these questions. anyone know the working outs?i saw the answer from the back of the book but i don't just want to copy it i want to understand it

    thanks.:]

    1)Two tanks contain equal amounts of water. They are connected by a pipe and 3000 litres of water is pumped from one tank to the other. One tank then contains 6 times as much water as the toher. How many litres of water did each tank contain originally.

    Answer:4200L

    2)a boy is 24 years younger than his father. In 2 years time the sum of thier ages will be 40. find the present ages of father and son.

    Answer: father-30 son-6

    3)A man travels from A to B at 4km/h and from B to A at 6km/h. the total journey takes 45 minutes. find the distance traveled

    answer- 3.6km

    4) jess walked for 45 minutes at 3km/h and then ran for half an hour at xkm/h. At the end of that time she was 6km from the starting point. find the value of x.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by fresh_ View Post
    2)a boy is 24 years younger than his father. In 2 years time the sum of thier ages will be 40. find the present ages of father and son.

    Answer: father-30 son-6
    Let the son's age be x. Then we know that the father's age is x + 24 years old.

    In two years the boy will be x + 2 years old and the father x + 24 + 2 = x + 26 years old. Then we know that
    (x + 2) + (x + 26) = 40

    2x + 28 = 40

    2x = 12

    x = 6

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by fresh_ View Post
    3)A man travels from A to B at 4km/h and from B to A at 6km/h. the total journey takes 45 minutes. find the distance traveled

    answer- 3.6km
    The relevant equation here is
    d = vt

    Let the distance from A to B (or B to A) be d.

    From A to B we have
    d = 4t
    where t is the take it takes for the trip.

    From B to A we have
    d = 6T
    where T is the time it takes for the trip.

    And we also know that
    t + T = 45~min = \frac{3}{4}~h

    (Use the unit hours for the time since the speed is given in km/h.)

    This gives you the three equations
    d = 4t
    d = 6T
    t + T = \frac{3}{4}

    -Dan
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  4. #4
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    [QUOTE=fresh_;162147]Hello I've received holiday homework from my text book and i cant seem to work ou these questions. anyone know the working outs?i saw the answer from the back of the book but i don't just want to copy it i want to understand it

    thanks.:]

    1)Two tanks contain equal amounts of water. They are connected by a pipe and 3000 litres of water is pumped from one tank to the other. One tank then contains 6 times as much water as the toher. How many litres of water did each tank contain originally.

    Answer:4200L


    Let us say each tank has x liters of water initially.
    So after 3000L is transfered from one tank to the other,
    one tank has now (x -3000) liters, and the other has (x +3000) liters.

    Then the problem says the tank with more water has now 6 times as much water than the tank with less water, meaning,
    (x +3000) = 6*(x -3000)

    So, simplifying that,
    x +3000 = 6x -18,000
    x -6x = -18,000 -3000
    -5x = -21,000
    x = -21,000 /(-5)
    x = 4200L -------same as the book answer.

    - - - - - - - -

    4) jess walked for 45 minutes at 3km/h and then ran for half an hour at xkm/h. At the end of that time she was 6km from the starting point. find the value of x.

    distance = rate * time
    d = rt

    The units must be consistent. If x is in km/hr, then time must be in hours.
    45minutes = 45/60 = 3/4 hr.

    (3/4)(3) +(1/2)(x) = 6 ------this is what the problem says.

    So,
    9/4 +x/2 = 6
    Clear the fractions, multiply both sides by 4,
    9 +2x = 24
    2x = 24 -9
    x = 15/2 = 7.5 ----------answer.
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  5. #5
    Newbie fresh_'s Avatar
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    THANKS GUYS FOR THE HELP!!, I REALLY NEEDED IT

    theirs one more i got stuck on for this exercise

    a shopkeeper buys a crate of eggs at $1.50 per dozen. He buys another crate, containing 3 dozen more than the first crate, at $2.00 per dozen. He sells them all for $2.50 a dozen and makes $15 profit. how many dozens were there in each of the crates.

    ANSWER- 9 AND 12 DOZEN

    THANKS AGAIN
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  6. #6
    Senior Member nikhil's Avatar
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    Here it is

    Quote Originally Posted by fresh_ View Post
    a shopkeeper buys a crate of eggs at $1.50 per dozen. He buys another crate, containing 3 dozen more than the first crate, at $2.00 per dozen. He sells them all for $2.50 a dozen and makes $15 profit. how many dozens were there in each of the crates.
    let there be x dozen eggs that he bought for 1.5$
    therfor his expenditure will be=1.5x $
    now he bought 3 dozen more eggs than before i.e x+3 for 2$ per dozen, therfor his expenditure will be=2(x+3)$
    so his total expenditure is
    [1.5x +2(x+3)]$
    now total dozen of eggs =x+x+3=2x+3 these were sold for 2.5$ per dozen therfor total selling price=2.5(2x+3) $
    (profit=total selling price-expenditure) profit is given to be=15$ therefor
    2.5(2x+3)-[1.5x +2(x+3)]=15
    5x+7.5-1.5x-2x-6=15
    1.5x=13.5
    x=9
    so intially there were 9 dozen eggs. Since second time shopkeeper took 3 dozen more eggs than previous time so second time there were 9+3=12 dozen eggs
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  7. #7
    Newbie fresh_'s Avatar
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    Quote Originally Posted by nikhil View Post
    let there be x dozen eggs that he bought for 1.5$
    therfor his expenditure will be=1.5x $
    now he bought 3 dozen more eggs than before i.e x+3 for 2$ per dozen, therfor his expenditure will be=2(x+3)$
    so his total expenditure is
    [1.5x +2(x+3)]$
    now total dozen of eggs =x+x+3=2x+3 these were sold for 2.5$ per dozen therfor total selling price=2.5(2x+3) $
    (profit=total selling price-expenditure) profit is given to be=15$ therefor
    2.5(2x+3)-[1.5x +2(x+3)]=15
    5x+7.5-1.5x-2x-6=15
    1.5x=13.5
    x=9
    so intially there were 9 dozen eggs. Since second time shopkeeper took 3 dozen more eggs than previous time so second time there were 9+3=12 dozen eggs
    thanks but this bit
    now total dozen of eggs =x+x+3=2x+3 how did you get the 3 ?
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