Jacob and sumalee each improved their yards by planting daylilies and geraniums. They bought their supplies from the same store. Jacob spent $107 on 11 daylilies and 4 geraniums. Sumalee spent $60 on 4 daylilies and 12 geraniums. Find the cost of one daylilies and the cost of one geranium.

Daylily: $9

Geranium: $2

Step-by-step explanation:

1 daylily costs x.

1 geranium costs y.

11x + 4y = 107

4x + 12y = 60

Multiply the first equation by 3 and subtract the second equation from it.

29x = 261

x = 9

4x + 12y = 60

4(9) + 12y = 60

12y = 24

y = 2

Daylily: $9

Geranium: $2

1) Set up a system of equations. Assign each plant a variable. I used X for Daylillies and Y for Geraniums. In this case:

11x + 4y = 107

4x + 12y = 60

2) Get one variable by itsef. You can choose to either get the X or the Y by itself. For the sake of ease, I'll go with achieving X.

3) Using the equation 4x + 12y = 60, isolate the 4x.

4x = -12y + 60

4) Divide both sides by 4.

x = -3y + 15

5) X is isolated. Now plug in that isolated X into another remaining equation in order to isolate Y. Don't forget to combine like terms.

11(-3y + 15) + 4y = 107

-33y + 165 + 4y = 107

-29y + 165 = 107

-29y = -58

y = 2

6) You have your Y, which means that each Geranium costs $2 each. Now, you need to find X. Plug in Y into any of the first two equations that we started with.

4x + 12(2) = 60

4x + 24 = 60

4x = 36

x = 9

7) You now have both X and Y. Daylillies cost $9 each, and Geraniums cost $2 each.

8) You can double-check your answers by plugging in your final X and Y values into any of the first equations you wrote. If it comes out equal, it works.

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