I make a strong and mild version chili dry rub. I mix $200$ g of red chili and $178$ g of sage to make $1$ strong dry rub. I mix $88$ g of red chili and $203$ g of sage to make a mild dry rub. I have $22$ kg of red chili and $13$ kg of sage in a two separate bottles left. Calculate how many kilogram of strong and mild I can make.
I attempted to make a chart: then express in system of linear equation.
- red chili Sage Result
- Mild $200$ g R $178$ g S 1 mild
- Strong $88$ g R $203$ g S 1 strong
- Left. $22$ kg R $13$ kg S = mild or strong
I want to express this in a system of linear equations.
$x=$ number of strong dry rub
$y=$ number of mild dry rub
$x(200r+178s)+y(88r+203s) = $ overall amount of substance
So if we expand out then:
$$200rx+88ry\leq22000$$ $$\therefore r(50x+22y)\leq5500$$
and
$$178sx+203sy\leq 13000$$ $$\therefore s(178x+203y)\leq13000$$
I'm really not sure if this is what you want (your question doesn't make much sense) but here are a few inequalities. If the exact $22kg$ and $13kg$ is meant to be used up then you can just replace the $\leq$ with $=$