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Heather and Amanda each improved their yards by planting rose brushes and germanium. They bought their supplies from the same store. Heather spent 50$ on 2 rose and 3 germaniums. Amanda spent 186$ on 6 rose bushes and 12 germaniums. What is the cost of one rose bush and the cost of one germanium

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sqdancefan

Answer:

  • rose bush: $7
  • geranium: $12

Step-by-step explanation:

You want the cost of one each of a rose bush and a geranium if 2 rose bushes and 3 geraniums cost $50, and 6 rose bushes and 12 geraniums cost $186.

Setup

Letting r and g represent the costs of a rose bush and a geranium, respectively, the two purchases can be represented by ...

  2r +3g = 50
  6r +12g = 186

Solution

Subtracting 3 times the first equation from the second, we have ...

  (6r +12g) -3(2r +3g) = (186) -3(50)

  3g = 36 . . . . . . simplify

  g = 12 . . . . . . . divide by 3

Then the cost of a rose bush can be found using the first equation:

  2r +3(12) = 50

  2r = 14 . . . . . . . . . . subtract 36

  r = 7 . . . . . . . . . . . divide by 2

The cost of a rose bush is $7; the cost of a geranium is $12.

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