Each Type S stone covers $0.30$ square meters and each Type L stone covers $0.50$ square meters, and together they cover $70$ square meters. How can you express this with $s$ and $l$?

If decimals feel messy, try multiplying the area equation by $10$ so that the coefficients become whole numbers. This often makes elimination easier.

Once you have two equations in $s$ and $l$, think about how to combine them so that $s$ disappears. What could you multiply one equation by so that when you subtract, the $s$ terms cancel?

In Desmos, let $x$ represent $s$ and $y$ represent $l$. In the first expression line, type x + y = 180 to represent the total number of stones.

In the next line, type 0.3x + 0.5y = 70 to represent the total area covered by the stones.

Look at the graph where the two lines intersect. Click on the intersection point; the coordinates will appear as $(x, y)$. The $y$-coordinate of this point is the number of Type L stones in the delivery.

We are told what $s$ and $l$ mean, so turn the words into equations:

• There are 180 stones total, so

• Each Type S stone covers $0.30$ square meters and each Type L stone covers $0.50$ square meters, and together they cover $70$ square meters, so

Now we have a system of two equations in two variables.

Work with whole numbers instead of decimals by multiplying the second equation by $10$:

So the system is now:

• $s + l = 180$
• $3s + 5l = 700$.

Eliminate $s$ by matching its coefficient in both equations.

Multiply the first equation by $3$:

Now subtract this new equation from $3s + 5l = 700$:

• Left side: $(3s + 5l) - (3s + 3l) = 2l$
• Right side: $700 - 540 = 160$

So you get a simple equation involving only $l$:

Solve $2l = 160$:

You can quickly find $s$ to check:

Check the total area:

square meters, which matches the problem.

So there are 80 Type L stones in the delivery.