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?

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:

7X + 3Y = 73 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.