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Algebra

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during a sale at the local department store, you buy three sweatshirts and two pairs of sweatpants for $85.50. later you return to the same store and but three more sweatshirts and four more pairs of sweatpants for $123. what is the sale price of each sweatshirt and each pair of sweatpants?

  • Algebra -

    3s + 4p = 123

    3s + 2p = 85.5

    Subtract second equation from the first.

    2p = 37.5

    p = 18.75

    You should be able to work it from here.

  • Algebra -

    3 sweatshirts and 2 sweatpants for 85.50 --> 3x+2y=85.50
    3 sweatshirts and 4 sweatpants for 123 --> 3x+4y=123
    solve for one of the variables in either equation (in terms of the other variable) and insert the answer into the other equation to get an actual value of the other variable

    3x+2y=85.5
    3x=85.5-2y
    x=(85.5-2y)/3
    x=28.5-(2/3)y --> insert the "x" value into the other equation to solve for "y"

    3(28.5-(2/3)y)+4y=123
    85.5-2y+4y=123
    2y=37.5
    y=18.75 --> now insert the "y" value into the first equation to get an actual value for "x"

    3x+2(18.75)=85.5
    3x+37.5=85.5
    3x=48
    x=16

    FINAL ANSWER:(x=16 and y=18.75)

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