Adam and Abhasra each improved their yards by planting rose bushes and geraniums. They bought their supplies from the same store. Adam spent $110 on 11 rose bushes and 4 geraniums. Abhasra spent $138 on 1 rose bush and 12 geraniums.

What is the cost of one rose bush and the cost of one geranium?

Question

High School

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Answer :

rakshadwivedi256se rakshadwivedi256se · Answer 1 · 2024-09-25T23:19:04-04:00

The cost of one rose bush is $6 and the cost of one geranium is $11.

To find the cost of one rose bush and one geranium, we need to solve the given equations. Let's assign variables to the unknowns:

Let the cost of one rose bush be R and the cost of one geranium be G.

From the given information:

Adam spent $110 on 11 rose bushes and 4 geraniums, so we have the equation: 11R + 4G = 110

Abhasra spent $138 on 1 rose bush and 12 geraniums, so we have the equation: R + 12G = 138

Now we can solve this system of equations to find the values of R and G. Here's how:

Multiplying the second equation by 11 to match the coefficients of R, we get: 11R + 132G = 1518

Subtracting the first equation from the modified second equation, we get: 132G - 4G = 1518 - 110

Simplifying, we have: 128G = 1408

Dividing both sides by 128, we find: G = 11

Substituting the value of G back into the first equation, we have: 11R + 44 = 110

Simplifying, we find: 11R = 66

Dividing both sides by 11, we find: R = 6

Therefore, the cost of one rose bush is $6 and the cost of one geranium is $11.