Algebra 2 Help Please!!

[Guest]

In preparation for this week’s orders for Fiery Sauce sauces, you bought 1050 green peppers and 1200 hot chili peppers.
- Write a system of inequalities (one inequality for each type of sauce) to represent how many pints you can make. Refer to the Red Hot Sauces and Scorchin’ Hot Sauce recipes below.
- Graph both inequalities on a coordinate grid.
- Select one possible solution of the system and determine how many peppers you will have left over.

Red Hot Sauce
Yields: 1 pint
1 pt tomato sauce with onions
5 green peppers, diced
4 hot chili peppers, seeded and diced

Scorchin’ Hot Sauce
Yields: 1 pint
1 pt tomato sauce with onions
4 green peppers, diced
8 hot chili peppers, seeded and diced

[HallsofIvy]

Let x be the number of pints of "red hot sauce" and y be the number of pints of "scorchin' hot sauce".

Each pint of "red hot sauce" requires 5 green peppers and each pint of "scorchin' hot sauce" requires 4 so you need 5x+ 4y green peppers. You have a total of 1050 green peppers so [tex]5x+ 4y\le 1050[/tex].

Each pint of "red hot sauce" requires 4 hot chili peppers and each pint of "scorchin' hot sauce' requires 8 so you need 4x+ 8y hot chili peppers. You have a total of 1200 hot chili peppers so [tex]4x+ 8y\le 1200[/tex]. You can simplify that a little by dividing each coefficient by 4: [tex]x+ 2y\le 300[/tex].

Each pint of "red hot sauce" requires 1 pint of "tomatoes with onions" and so does each pint of "scorchin' hot sauce" so x and y pints will require x+ y pints of "tomatoes with onions" but we are not told how much "tomatoes with onions" so we do not get an inequality from this.