Algebra 1 word problem

Question

Lea and Brenda each improved their yards by planting grass sod and ornamental grass. They

bought their supplies from the same store. Lea spent $171 on 13 ft² of grass sod and 5 bunches

of ornamental grass. Brenda spent $90 on 5 ft² of grass sod and 10 bunches of ornamental grass.

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

Answer 1

Juliana,

Since there are two variables (sod and ornamental grass) in this question, you need to assign variables to the two. Let's use x for square feet of sod and y for bunches of grass.

Lea's purchase can now be written as 171=13x+5y.

In the same fashion, Brenda's purchase for $90 is represented by

90=5x+10y.

I used x and y as variables because it's easy to graph these on a tool like Desmos.com to find the answer.

I solved it quickly, however, using the "elimination method" for solving systems of equations. Given

171=13x+5y and

90 = 5x +10y, I multiplied the first equation by -2: -2(171=13x+5y) = -342=-26x-10y.

This allows me to add the equations and eliminate one variable:

-342=-26x-10y

+ 90 = 5x +10y

-252 = -21x Divide both sides by -21 to solve for x.

12 = x Now we have the cost of sod. One square foot of sod is $12.

Plug that into an original equation to get the cost of a bunch of grass:

90 = 5(12)+10y

90 = 60 +10y. Subtract 60 from both sides and divide by 10 to find y= $3.

I hope this helps, and have fun mathing!

LizZ