Question

1. shreya and ted each improved their yards by planting grass sod and ornamental grass. they bought their supplies from the same store. shreya spent $174 on 13 m² of grass sod and 12 bunches of ornamental grass. ted spent $90 on 11 m² of grass sod and 3 bunches of ornamental grass. find the cost of one m² of grass sod and the cost of one bunch of ornamental grass.

Explanation:

Step1: Set up equations

Let the cost of one $m^2$ of grass sod be $x$ dollars and the cost of one bunch of ornamental grass be $y$ dollars.
For Ted: $11x + 3y=90$.
For Shreya: $13x + 12y = 174$.

Step2: Multiply the first - equation to eliminate $y$

Multiply the equation $11x + 3y=90$ by 4. We get $44x+12y = 360$.

Step3: Subtract the second equation from the new - first equation

$(44x + 12y)-(13x + 12y)=360 - 174$.
$44x+12y - 13x - 12y=186$.
$31x=186$.
$x = 6$.

Step4: Substitute $x$ into the first equation to find $y$

Substitute $x = 6$ into $11x+3y = 90$.
$11\times6+3y=90$.
$66+3y=90$.
$3y=90 - 66$.
$3y=24$.
$y = 8$.

Answer:

The cost of one $m^2$ of grass sod is $\$6$ and the cost of one bunch of ornamental grass is $\$8$.