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Answer :
Final answer:
By solving a system of linear equations using the elimination method, it's determined that the cost of one rose bush is $9 and the cost of one geranium is $10.
Explanation:
The question involves solving a system of linear equations to find the cost of one rose bush and the cost of one geranium. We can establish two equations from the information given:
1) 10R + G = 100
2) 8R + 7G = 142
To solve for R and G, we can use either substitution or elimination method. Let's use the elimination method by multiplying the first equation by 7 to make the coefficients of G the same:
7(10R + G) = 700
10R + 7G = 142
This gives us:
70R + 7G = 700
8R + 7G = 142
Subtracting the second equation from the first yields:
(70R - 8R) + (7G - 7G) = (700 - 142)
62R = 558
Dividing both sides by 62 gives us the price of one rose bush:
R = 558 \/ 62
R = 9
Now, substitute R = 9 into the first equation to find G:
10(9) + G = 100
90 + G = 100
G = 100 - 90
G = 10
Hence, the cost of one rose bush is $9, and the cost of one geranium is $10.
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