Answer :
Answer:
Cost of 1 rose bush = x = $5
Cost of 1 geraniums = y = $2
Step-by-step explanation:
DeShawn and Mike each improved their yards by planting rose bushes and geraniums. They bought their supplies from the same store.
Let us represent:
Cost of 1 rose bush = x
Cost of 1 geraniums = y
DeShawn spent $13 on 1 rose bush and 4 geraniums.
x + 4y = 13..... Equation 1
x = 13 - 4y
Mike spent $56 on 10 rose bushes and 3 geraniums.
10x + 3y = 56....... Equation 2
We substitute 13 - 4y for x in Equation 2
10(13 - 4y) + 3y = 56
130 - 40y + 3y = 56
Collect like terms
- 40y + 3y = 56 - 130
-37y = -74
y = -74/37
y = $2
Solving for x
x = 13 - 4y
x = _13 - 4 × $2
x = $13 - $8
x = $5
Therefore,
Cost of 1 rose bush = x = $5
Cost of 1 geraniums = y = $2
Final answer:
By setting up a system of equations based on the purchases and using the elimination method, it is found that the cost of one rose bush is $5 and the cost of one geranium is $2.
Explanation:
The question involves solving a system of equations based on the information given about DeShawn and Mike's purchases of rose bushes and geraniums. To find the cost of one rose bush and one geranium, we set up two equations based on the given scenarios.
- Equation 1 (DeShawn's purchase): 1R + 4G = $13, where R represents the cost of a rose bush and G represents the cost of a geranium.
- Equation 2 (Mike's purchase): 10R + 3G = $56.
To solve this system, we can use either substitution or elimination method. Here, we'll use the elimination method for simplicity.
- Multiply Equation 1 by 10 to make the coefficients of R the same: 10R + 40G = $130.
- Subtract Equation 2 from this new equation: (10R + 40G) - (10R + 3G) = $130 - $56, simplifying to 37G = $74.
- Solve for G: G = $2.
- Substitute the value of G in one of the original equations to find R. Using Equation 1, 1R + 4(2) = $13 → R = $5.
Therefore, the cost of one rose bush is $5 and the cost of one geranium is $2.
