Suppose you buy flour and cornmeal in bulk to make flour tortillas and corn tortillas flour costs 1.50lb cornmeal costs 2.50lb you want to spend less than 9.50 on flour and cornmeal and you need at least 4lb altogether

a) write a system of inequalities that describes this situation
b) graph the system to show all possible solutions

f+c >= 4

1.50f + 2.50c <= 9.5

for graphing help, visit wolframalpha.com and enter

solve f+c >= 4, 1.50f + 2.50c <= 9.5

a) To write a system of inequalities that describes this situation, we first need to define the variables. Let F represent the amount of flour in pounds, and let C represent the amount of cornmeal in pounds.

The given information implies the following conditions:
1. The cost of flour is $1.50 per pound, so the cost of F pounds of flour would be 1.50F.
2. The cost of cornmeal is $2.50 per pound, so the cost of C pounds of cornmeal would be 2.50C.
3. You want to spend less than $9.50 on flour and cornmeal combined, which can be represented as 1.50F + 2.50C < 9.50.
4. You need at least 4 pounds of flour and cornmeal altogether, which can be represented as F + C ≥ 4.

Therefore, the system of inequalities that describes this situation is:
1.50F + 2.50C < 9.50
F + C ≥ 4

b) To graph the system, we can convert each inequality into an equation and plot the corresponding lines.

For the first inequality, 1.50F + 2.50C < 9.50, we can rearrange it as follows:
1.50F + 2.50C = 9.50

To simplify this equation, we can multiply everything by 2 to get rid of the decimal:
3F + 5C = 19

Now, let's graph this equation:

Plotting this equation on a coordinate plane, you can draw a line with an intercept at (0, 3.8) and a slope of (-5/3), as this line represents the inequality 1.50F + 2.50C < 9.50.

Next, let's graph the second inequality, F + C ≥ 4.

Plotting this equation on the same coordinate plane, we can draw a line with an intercept at (4, 0) and a slope of (-1).

Finally, shade the region that satisfies both inequalities. This region will include all the points that are below the line 1.50F + 2.50C = 9.50 and to the right of the line F + C = 4.

The shaded region represents all possible solutions for the amount of flour and cornmeal that you can buy while meeting the given conditions.