Answer :
Final answer:
The cost for each plant is $2 for a rose bush and $3 for a geranium.
Explanation:
In order to find the cost for each plant, we can set up a system of equations. Let's let x represent the cost of a rose bush and y represent the cost of a geranium. According to the given information, we can write the following equations:
13x + 7y = 47 (Equation 1)
7x + 10y = 44 (Equation 2)
We can solve this system of equations using the method of substitution or elimination. For simplicity, let's use the method of substitution. We can solve Equation 1 for x and substitute it into Equation 2:
13x = 47 - 7y
x = (47 - 7y)/13
Substituting this value of x into Equation 2:
7((47 - 7y)/13) + 10y = 44
Simplifying this equation:
(329 - 49y)/13 + 10y = 44
Multiplying through by 13 to eliminate the fraction:
329 - 49y + 130y = 572
Combining like terms:
81y = 243
Simplifying:
y = 3
Substituting this value of y back into Equation 1:
13x + 7(3) = 47
13x + 21 = 47
13x = 26
x = 2
So, the cost for each plant is $2 for a rose bush and $3 for a geranium.
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