At a local garden shop, the price of plants includes
sales tax. The cost of 4 large plants and 8 medium
plants is $40. The cost of S large plants and 2
medium plants is $28. If / is the cost of a large
plant and m is the cost of a medium plant, write a
system of equations that models this situation.
Could the cost of one large plant be $5.50 and the
cost of one medium plant be $2.25? Justify your
answer. Determine algebraically both the cost of a
large plant and the cost of a medium plant.

Equation (1) and equation (2) represent the system of equations, the cost of the large plant is $4.5, and the cost of the medium plant is $2.75

What is a linear equation?

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

We have:

l is the cost of a large plant and m is the cost of a medium plant.

The cost of 4 large plants and 8 medium plants is $40.

For the above scenario, the linear expression can be written as in two variables:

4l + 8m = 40 ...(1)

The cost of 5 large plants and 2 medium plants is $28 for this scenario, the linear expression can be written as in two variables:

5l + 2m = 28 ...(2)

Multiplying the above equation with 4 on both sides

20l + 8m = 112 ...(3)

Subtracting equation (1) from equation (2), we get:

20l - 4l = 112 - 40

16l = 72

l = $4.5

Put this value in the equation (1), we get:

4(4.5) +8m = 40

18 +8m = 40

m = $2.75

Thus, the equation (1) and equation (2) represent the system of equations, the cost of the large plant is $4.5, and the cost of the medium plant is $2.

Learn more about the linear equation here:

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