Shawna and Micaela each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Shawna spent $171 on 12 m² of grass sod and 13 geraniums. Micaela spent $90 on 6 m² of grass sod and 8 geraniums.

Find the cost of one m² of grass sod and the cost of one geranium.

To find the cost of one m² of grass sod and the cost of one geranium, set up a system of equations and solve for the variables. The cost of one m² of grass sod is $11 and the cost of one geranium is $3.

Explanation:

To find the cost of one m² of grass sod and the cost of one geranium, we can set up a system of equations using the given information.

Let x be the cost of one m² of grass sod and y be the cost of one geranium.

From the information given, we can write the following equations:

12x + 13y = 171

6x + 8y = 90

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

Solve for x in terms of y in one of the equations:

From the second equation, we can solve for x:

6x = 90 - 8y

x = 15 - (4/3)y

Substitute the expression for x in terms of y into the other equation:

12(15 - (4/3)y) + 13y = 171

180 - 16y + 13y = 171

-3y = -9

y = 3

Substitute the value of y into the expression for x to find the cost of one m² of grass sod:

x = 15 - (4/3)(3)

x = 15 - 4

x = 11

Therefore, the cost of one m² of grass sod is $11 and the cost of one geranium is $3.