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Castel and Huong each improved their yards by planting grass sod and ornamental grass. They bought their supplies from the same store.

Castel spent $144 on 6 ft² of grass sod and 9 bunches of ornamental grass. Huong spent $151 on 9 ft² of grass sod and 7 bunches of ornamental grass.

What is the cost of one ft² of grass sod and the cost of one bunch of ornamental grass?

The cost of one ft² of grass sod is $[Select], and the cost of one bunch of ornamental grass is $[Select].

Answer :

By setting up and solving a system of linear equations, we find that the cost of one square foot of grass sod is $9 and the cost of one bunch of ornamental grass is $10.

The problem presented is a classic example of a system of linear equations. We have two equations derived from the information provided:

Castel: 6s + 9o = $144

Huong: 9s + 7o = $151

Where s represents the cost per square foot of grass sod, and o represents the cost per bunch of ornamental grass. To solve for s and o, we can use a method like substitution or elimination.

Multiply the first equation by 3 and the second equation by 2 to eliminate o:

(3) 6s + 9o = 432

(2) 9s + 7o = 302

Now, we subtract the second resulting equation from the first:

18s + 27o = 432

18s + 14o = 302

After subtraction:

13o = 130

o = $10

We can then substitute the value of o into any of the original equations to find the cost of sod per square foot:

6s + 9(10) = $144

6s = $54

s = $9

Therefore, the cost of one ft' of grass sod is $9 and the cost of one bunch of ornamental grass is $10.

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Rewritten by : Barada

The cost of one ft' of grass sod is $9 and the cost of one bunch of ornamental grass is $10.

How to illustrate the information?

Based on the information, the appropriate equation will be:

6g + 9y = 144

9g + 7y = 151

where g = grass sod

o = ornamental grass

Multiply equation I by 9

Multiply equation ii by 6

54g + 81y = 1296

54g + 42y = 906

Subtract

39y = 390

y = 390/39

y = 10

From 9g + 7y = 151

9g + 7(10) = 151

9g = 151 - 70

9g = 81

g = 81/9

g = 9

Therefore, the cost of one ft' of grass sod is $9 and the cost of one bunch of ornamental grass is $10.

Learn more about equations on:

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