Linear inequalities

Question

Cherries cost $4/lb. Grapes cost $2.50/lb. you can spend no more than $15 on fruit, and you need at least 4 lb in all. Create a graph showing the amount of each fruit you can buy.

Answer 1

Agree with explanation, just clarifying: the solution is a common intersecting area of both shades where they overlay each other.

To draw the inequalities bring them to slope/intercept form: y = mx + b, then the cost inequality will become;

y ≤ - 1.6x + 6   and pounds inequality:  y ≥ - x - 4. 

 

Both lines will be falling down, for the first line shadow below the line (as the sign is ≤) and for the second shadow over the line. Intersection area of two shadows is your solution. 

 

Do not have tools to insert that graph here. 

 

Regina G 

Answer 2

Let x = the number of cherries in pounds

Let y = the number of grapes in pounds

 

Using these variables, we can create a system of inequalities.

 

4x + 2.5y ≤ 15         ineq1 ----> total cost

 

x + y ≥ 4           ineq2  ---> total pounds

 

 

These are your inequalities.  When you graph the inequalities, shade in the region that is below then first inequality, but greater than the second inequality.  The shaded region is the solution set.

FYI, cherries and grapes are not fruits. They are berries.