Suppose you buy flour and cornmeal in bulk to make flour tortillas and corn tortillas. Flour costs $1.50/lb. Cornmeal costs $2.50/lb. You want to spend less than $9.50 on flour and cornmeal, and you need at least 4 lb altogether. Write a system of inequalities that describes this situation.

Question

Suppose you buy flour and cornmeal in bulk to make flour tortillas and corn tortillas. Flour costs $1.50/lb. Cornmeal costs $2.50/lb. You want to spend less than $9.50 on flour and cornmeal, and you need at least 4 lb altogether. Write a system of inequalities that describes this situation.

I wrote my two equations:

1.x+y¡Ý4
4¡Ý-x+4

2. 1.5x+2.5y<9.5
1.5x+2.5(-x+4)<9.5
1.5-2.5x+10<9.5
-x+10<9.5
-x<9.5-10
-x<-0.5
x>0.5

I solved the 2nd equation, but what am I supposed to do with the first one now?

Answer 1

never mind, i get it, i wasn't supposed to solve any equations at all..

Answer 2

54x^2y^13/-2x^5y^-2

Answer 3

To solve the first equation, you need to find the valid range of values for the variables x and y that satisfies the given conditions.

The first equation, x + y ≥ 4, represents the condition that the total amount of flour and cornmeal you purchase should be at least 4 pounds. This means you can use at least 4 pounds of flour and cornmeal combined to make your tortillas.

To solve this inequality, you can use either the substitution method or graphing method. Let's use the graphing method to visualize the solution.

First, rewrite the inequality in slope-intercept form by isolating y:

y ≥ -x + 4

Now, graph the line y = -x + 4. This line has a slope of -1 and y-intercept of 4.

To graph it, you can start by plotting the y-intercept (0, 4). Then, using the slope of -1, move one unit down and one unit to the right to find another point. Connect these two points to draw the line.

Now, since you need the solution where x + y ≥ 4, the valid region is the area above or on the line y = -x + 4. Shade the region above or on the line to represent this.

Next, consider the second equation you solved: x > 0.5. This inequality represents the condition that the amount of flour (x) should be more than 0.5 pounds.

To represent this graphically, draw a vertical line at x = 0.5 on the x-axis.

Now, look at the area where both conditions are satisfied. This will be the region that is above or on the line y = -x + 4, and to the right of the vertical line x = 0.5. Shade this region to represent the solution.

The shaded region will be the final solution to the system of inequalities:

x + y ≥ 4
x > 0.5

This means any combination of values for x and y within the shaded region will satisfy the conditions of spending less than $9.50 and needing at least 4 pounds of flour and cornmeal combined.