Richie spent $120 on 12 rose bushes and 2 gardenias, while Jim spent 3150 on 10 rose bushes and 10 gardenias. What is the cost of 1 rose bush and 1 gardenia?

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Richie spent  $120 on 12 rose bushes and 2 gardenias, while Jim spent 3150 on 10 rose bushes and 10 gardenias. What is the cost of 1 rose bush and 1 gardenia?

Bytelearn · Accepted Answer

Equation for Richie's purchase: Let's denote the cost of one rose bush as R dollars and the cost of one gardenia as G dollars. Richie's purchase can be represented by the equation: 12R + 2G = 120 dollars.Equation for Jim's purchase: Similarly, Jim's purchase can be represented by the equation: 10R + 10G = 3150 dollars.Elimination method: To solve for R and G, we can use the method of substitution or elimination. Let's use elimination. First, we'll multiply Richie's equation by 5 to align the G terms with Jim's equation: (12R + 2G) * 5 = 120 * 5 60R + 10G = 600Subtract equations: Now we have two equations: 60R + 10G = 600 (Richie's equation multiplied by 5) 10R + 10G = 3150 (Jim's equation) We can subtract Jim's equation from the modified Richie's equation to eliminate G: (60R + 10G) - (10R + 10G) = 600 - 3150 50R = -2550Solve for R: Dividing both sides of the equation by 50 to solve for R: 50R / 50 = -2550 / 50 R = -51 We have a negative value for the cost of a rose bush, which doesn't make sense in this context. There must be a mistake in the previous steps.

Richie spent $\$ 120$ on $12$ rose bushes and $2$ gardenias, while Jim spent $3150$ on $10$ rose bushes and $10$ gardenias. What is the cost of $1$ rose bush and $1$ gardenia?

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Richie spent $\$ 120$ on $12$ rose bushes and $2$ gardenias, while Jim spent $3150$ on $10$ rose bushes and $10$ gardenias. What is the cost of $1$ rose bush and $1$ gardenia?