Question

Kelly and Trisha are planting new flowers in the school courtyard. Kelly bought 1 rose bush and 14 daisies for a total of $121. Trisha bought 8 rose bushes and 13 daisies for a total of $176. What is the cost of one rose bush and one daisy?

Answer 1

The cost of one rose bush is $9, and the cost of one daisy is $8. This was determined by setting up a system of linear equations based on Kelly and Trisha's purchases, and then using the elimination method to solve for the individual prices of a rose bush and a daisy.

Step-by-step explanation:

The question involves the system of linear equations where Kelly and Trisha's purchases are represented by two equations. Let's define the cost of one rose bush as R dollars and the cost of one daisy as D dollars. Kelly's purchase gives us the equation R + 14D = 121, and Trisha's purchase gives us 8R + 13D = 176.

To find the value of R and D, we can use the method of substitution or elimination. We will use the elimination method in this case. Multiplying the first equation by 8 gives us 8R + 112D = 968. We then subtract Trisha's equation from this new equation to eliminate R and solve for D.

1. 8R + 112D = 968 (Kelly's equation multiplied by 8)
2. 8R + 13D = 176 (Trisha's equation)
3. Subtract the second equation from the first: (112D - 13D = 968 - 176)
4. 99D = 792
5. D = $8 (cost of one daisy)
6. Using the value of D in Kelly's original equation: R + 14(8) = 121
7. R + 112 = 121
8. R = $9 (cost of one rose bush)

Therefore, the cost of one rose bush is $9 and the cost of one daisy is $8.