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Lea and Julio each improved their yards by planting rose bushes and geraniums. They bought their supplies from the same store. Lea spent $74 on 4 rose bushes and 6 geraniums. Julio spent $172 on 11 rose bushes and 12 geraniums.

Find the cost of one rose bush and the cost of one geranium.

Answer :

Final answer:

To find the cost of one rose bush and one geranium, we use the information given to establish a system of equations. By solving the system, we determine that the cost of one rose bush is $8 and the cost of one geranium is $7.

Explanation:

The question involves finding the cost of one rose bush and the cost of one geranium using a system of equations. We will let the variable r represent the cost of one rose bush and g represent the cost of one geranium. Lea's purchase gives us the first equation, 4r + 6g = $74. Julio's purchase gives us the second equation, 11r + 12g = $172. We can solve this system of equations using methods such as substitution, elimination, or algebraic solutions.

Step-by-Step Solution:

Write the equations based on the given information:4r + 6g = 74 (1)11r + 12g = 172 (2)
  1. Choose an equation to manipulate to solve for one variable. Let's multiply equation (1) by 2 to eliminate g:
    8r + 12g = 148 (3)
  2. Subtract equation (3) from equation (2):
    (11r + 12g) − (8r + 12g) = 172 − 148
    3r = 24
    r = 24/3
    r = $8
  3. Substitute the value of r back into equation (1):
    4(8) + 6g = 74
    32 + 6g = 74
    6g = 74 − 32
    6g = 42
    g = 42/6
    g = $7

Therefore, one rose bush costs $8 and one geranium costs $7.

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