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Math Help - Problem solving?

  1. #1
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    Unhappy Problem solving?

    Kim placed an order for 98 gizmos which cost $445. A package of 7 gizmos cost $30, and a package of 5 gizmos cost $25. How many packages of each type did Kim order?

    Really not sure how to start it from there.. and how to put it into equations.
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  2. #2
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    Hi fvaras89

    Let :
    x = package of 7 gizmos
    y = package of 5 gizmos

    1.
    If Kim buys one x and one y, she will get 12 gizmos -----> 7*1 + 5*1 = 12
    If Kim buys two x and one y, she will get 19 gizmos -----> 7*2 + 5*1 = 19
    If Kim buys three x and two y, she will get 31 gizmos -----> 7*3 + 5*2 = 31

    If Kim has to buy 98 gizmos, can you find the equation ? ----> 1st equation


    2.
    If Kim buys one x and one y, she will spend $55 -----> 30*1 + 25*1 = 55
    If Kim buys two x and one y, she will spend $85 -----> 30*2 + 25*1 = 85
    If Kim buys three x and four y, she will spend $190 -----> 30*3 + 25*4 = 190

    If Kim has $445, can you find the equation ? -------> 2nd equation

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  3. #3
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    Quote Originally Posted by fvaras89 View Post
    Kim placed an order for 98 gizmos which cost $445. A package of 7 gizmos cost $30, and a package of 5 gizmos cost $25. How many packages of each type did Kim order?

    Really not sure how to start it from there.. and how to put it into equations.
    Let x be the number of 7 gizmo packets and y be the number of 5 gizmo packets bought. Then:

    7x + 5y = 98 .... (1)

    30x + 25y = 445 .... (2)

    Solve simultaneously.
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  4. #4
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    Okay thanks, i solved them simultaneously and i got

    7x + 5y = 98 (1)
    30x + 25y = 445 (2)

    (1) * 5

    35x + 25y = 490 (3)

    (3) - (2)

    5x = 45
    x = 9

    then substitute into (1)

    7(9) + 5y = 98
    63 + 5y = 98
    5y = 35
    y = 7

    Is that correct?
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  5. #5
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    Quote Originally Posted by fvaras89 View Post
    Okay thanks, i solved them simultaneously and i got

    7x + 5y = 98 (1)
    30x + 25y = 445 (2)

    (1) * 5

    35x + 25y = 490 (3)

    (3) - (2)

    5x = 45
    x = 9

    then substitute into (1)

    7(9) + 5y = 98
    63 + 5y = 98
    5y = 35
    y = 7

    Is that correct?
    Does your solution work when you substitute it into the two equations? Check that and then you'll know.
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  6. #6
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    oh yes it does!!! thanks heaps to you both
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