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Math Help - linear lines and problems

  1. #1
    Newbie white's Avatar
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    Exclamation linear lines and problems

    hello i need help on a few quesitons.

    the straight line with equation ax+by=c passes through the points (2,4) and (-3,1). find the values of a,b,c.

    wheel rite, a small company that manufactures garden wheelbarrows, has overhead expenses of $30 000 per year. in addition, it cost $40 to manufacture each wheelbarrow
    a- how many wheelbarrows must be made so that the overall cost is $46 per wheelbarrow?
    b- what is the minimum number of wheelbarrows that must be produced for wheel rite of make profit each year?

    thank you in advance
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  2. #2
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    Quote Originally Posted by white View Post
    hello i need help on a few quesitons.

    the straight line with equation ax+by=c passes through the points (2,4) and (-3,1). find the values of a,b,c.
    The two co-ordinates are: (2, 4) and (3, -1).

    m = \frac{y_1-y_2}{x_1 - x_2} =  \frac{4-(-1)}{2-3} = \frac{5}{-1}= -5

    y-y_1 = m (x - x_1) \implies  y-4 = -5(x-2) \therefore y=-5x+14.

    As ax+by=c is 5x + y =14 \implies a=5, b=1, c=14
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  3. #3
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    Quote Originally Posted by white View Post
    hello i need help on a few quesitons.

    the straight line with equation ax+by=c passes through the points (2,4) and (-3,1). find the values of a,b,c.

    Mr F says: There's not enough information to get unique numerical values of a, b and c. There's an infinite number of possible solutions. The best that can be done is to express two of a, b and c in terms of the third.

    Note: One of the infinite number of possible solutions is a = 5, b = 1, c = 14 (Given by Air). Another is a = 10, b = 2, c = 28 .......



    wheel rite, a small company that manufactures garden wheelbarrows, has overhead expenses of $30 000 per year. in addition, it cost $40 to manufacture each wheelbarrow
    a- how many wheelbarrows must be made so that the overall cost is $46 per wheelbarrow?

    Mr F says: Cost to make x wheel barrows is 30,000 + 40x. Therefore overall cost per barrow is (30,000 + 40x)/x. Solve (30,000 + 40x)/x = 46 ........

    b- what is the minimum number of wheelbarrows that must be produced for wheel rite of make profit each year?

    Mr F says: Are you selling at $46 per barrow? Then solve 46y > 30,000 + 40y for the smallest integer value of y. Note: You break even when y = x (the answer to a).

    thank you in advance
    ..
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  4. #4
    Newbie white's Avatar
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    hey i found out y >5000 now what ?
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  5. #5
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    Quote Originally Posted by white View Post
    hey i found out y >5000 now what ?
    If you sell at $46/barrow you make a profit when you sell more than 5000. So the minimum number you need to sell to make a profit is ....... ?
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