Question

Beth and James each improved their yards by planting rose bushes and geraniums. They bought their supplies from the same store. Beth spent $86 on 10 rose bushes and 3 geraniums. James spent $24 on 1 rose bush and 8 geraniums.

Write a system of equations that models this scenario. Using the table, determine the cost of one rose bush and one geranium

Answer 1

The cost of one rose bush is $8 and the cost of one geranium is $2, determined by setting up and solving a system of equations representing Beth's and James' purchases.

Step-by-step explanation:

Beth and James are working on their yards and have purchased various amounts of rose bushes and geraniums. To find the cost of one rose bush and one geranium, we can set up a system of equations based on the information provided. Beth's purchase can be represented by the equation 10r + 3g = 86, and James' purchase by the equation r + 8g = 24, where r is the cost of a rose bush and g is the cost of a geranium

To solve this system, we can use either substitution or elimination. Let's use the elimination method. By multiplying the second equation by -10, we get -10r - 80g = -240. Adding this to the first equation cancels out the r variable:

• 10r + 3g = 86
• -10r - 80g = -240

This results in -77g = -154. Dividing both sides by -77 gives g = 2. Now that we know the cost of a geranium, we can substitute this value back into one of the original equations to find the cost of a rose bush. Using the second equation, r + 8(2) = 24 simplifies to r + 16 = 24. Subtracting 16 from both sides gives us r = 8.

Therefore, one rose bush costs $8 and one geranium costs $2.