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Brenda and Ted each improved their yards by planting daylilies and geraniums. They bought
their supplies from the same store. Brenda spent $73 on 7 daylilies and 3 geraniums. Ted spent
$117 on 3 daylilies and 12 geraniums. What is the cost of one daylily and the cost of one
geranium?

Respuesta :

yersanabria

Answer:

The cost of the flowers is:

  • Daylily = $7
  • Geranium = $8

Step-by-step explanation:

First we use the next variables:

  • Daylily Cost = X
  • Geranium Cost = Y

With the information in the paragraph we can do the next formulas:

  1. 7X + 3Y = 73
  2. 3X + 12Y = 117

We clear the variable X in the first formula:

  • 7X + 3Y = 73
  • 7X = 73 - 3Y
  • X = (73 - 3Y)/7

And we replace the X in the second formula:

  • 3X + 12Y = 117
  • 3((73 - 3Y)/7) + 12Y = 117

Now we operate:

  • ((219 - 9Y)/7) + 12Y = 117
  • (219 - 9Y + 84Y)/7 = 117
  • 219 + 75Y = 117 * 7
  • 219 + 75Y = 819
  • 75Y = 819 - 219
  • 75Y = 600
  • Y = 600/75
  • Y = 8

In the last step, we can replace the Y in the first formula:

  • 7X + 3Y = 73
  • 7X + 3(8) = 73
  • 7X + 24 = 73
  • 7X = 73 - 24
  • 7X = 49
  • X = 49/7
  • X = 7

Then, how X is the daylily cost, this is $7 and how Y is the geranium cost, this is $8.