Question

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?

Answer 1

The cost of the flowers is:

• Daylily = $7
• Geranium = $8

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.