Question

Amy and Natalie each improved their yards by planting grass sod and ivy. They bought their supplies from the same store. Amy spent $137 on 11 ft^2 of grass sod and 6 pots of ivy. Natalie spent $190 on 10 ft^2 of grass sod and 12 pots of ivy. Find the cost of one ft^2 of grass sod and the cost of one pot of ivy.

A) Grass sod: $10/ft^2, Ivy: $3/pot
B) Grass sod: $12/ft^2, Ivy: $5/pot
C) Grass sod: $11/ft^2, Ivy: $4/pot
D) Grass sod: $9/ft^2, Ivy: $6/pot

Answer 1

The cost of one ft^2 of grass sod is $7 and the cost of one pot of ivy is $10.

Step-by-step explanation:

To find the cost of one ft2 of grass sod and the cost of one pot of ivy, we need to set up a system of equations based on the given information.

Let's assume the cost of one ft2 of grass sod is x dollars and the cost of one pot of ivy is y dollars. From the information given, we can set up the following equations:

1. 11x + 6y = 137 (equation 1)
2. 10x + 12y = 190 (equation 2)

Now, we can solve this system of equations to find the values of x and y.

Multiplying equation 1 by 10 and equation 2 by 11, we get:

1. 110x + 60y = 1370
2. 110x + 132y = 2090

Subtracting equation 2 from equation 1, we get

72y = 720

Dividing both sides by 72, we find that y = 10.

Substituting the value of y back into equation 1, we can solve for x:

11x + 6(10) = 137

11x + 60 = 137

11x = 77

Dividing both sides by 11, we find that x = 7.

Therefore, the cost of one ft2 of grass sod is $7 and the cost of one pot of ivy is $10.