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Bill and Heather each improved their yards by planting rose bushes and geraniums. They bought their supplies from the same store.

- Bill spent $47 on 13 rose bushes and 7 geraniums.
- Heather spent $44 on 7 rose bushes and 10 geraniums.

What is the cost for each plant?

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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