Answer :
The cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.
To find the cost of one hosta and one geranium, we can set up a system of equations based on the given information.
Let's assume the cost of one hosta is represented by 'h' and the cost of one geranium is represented by 'g'.
From the information given, we can set up the following equations:
Eugene's spending:
18h + 6g = $150
Jessica's spending:
7h + 16g = $113
We can now solve this system of equations to find the values of 'h' and 'g'.
Multiplying the first equation by 2 and the second equation by 3 to eliminate 'g', we get:
36h + 12g = $300
21h + 48g = $339
Now, we can subtract the second equation from the first to eliminate 'h':
(36h + 12g) - (21h + 48g) = $300 - $339
36h - 21h + 12g - 48g = -$39
15h - 36g = -$39
Simplifying further, we have:
15h - 36g = -$39
Now we can solve this equation for 'h' and substitute the value back into any of the original equations to find 'g'.
Let's solve for 'h':
15h = 36g - $39
h = (36g - $39) / 15
Substituting this value of 'h' into Eugene's equation:
18[(36g - $39) / 15] + 6g = $150
(648g - $702) / 15 + 6g = $150
648g - $702 + 90g = $150 * 15
738g - $702 = $2250
738g = $2250 + $702
738g = $2952
g = $2952 / 738
g ≈ $4
Now, substituting the value of 'g' back into Eugene's equation:
18h + 6($4) = $150
18h + $24 = $150
18h = $150 - $24
18h = $126
h = $126 / 18
h ≈ $7
Therefore, the cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.
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