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You are planning an ornamental garden that has a total area of 200 square feet. There are two sizes of ornamental plants you have chosen for your garden. Each small plant requires 2.5 square feet of space and each large plant requires 8 square feet of space. This situation can be modeled by the equation where x is the number of small plants and y is the number of large plants to be placed in the garden.

1.What are 3 possibliities of small plants and large plants you can plant in the garden?

  • algebra - ,

    2.5x + 8y = 200
    5x + 16y = 400

    We can graph this on the x-y plane and only look what the line does in the first quadrant.

    x-intercept, let y = 0 , x = 80
    y intercept , let x = 0 , y = 25

    slope of line = -25/80 = -5/16
    So starting with the point (80,0)
    we can decrease the x by 16 and increase the y by 5 to get a new point
    ---> (64, 5)
    ---> (48, 10)
    ---> (32, 15)
    ---> (16, 20)
    ---> (0, 25)

    pick any 3

    testing one of them:
    e.g. (32,15)
    32 small + 15 large
    takes 32(2.5) + 15(8) = 200

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