Cherries coat $4/lb. Grapes cost $2.50/lb. You can spend no more than $15 on fruit, and you need at least 5 lb in all. Create a graph showing the amount of each fruit you can buy.
To create a graph showing the amount of each fruit you can buy, we can use a coordinate plane with the x-axis representing the weight of cherries (in lbs) and the y-axis representing the weight of grapes (in lbs).
First, we need to determine the maximum weight of cherries and grapes we can buy. Let's assume we buy x lb of cherries and y lb of grapes.
From the given information, we have the following constraints:
1. We can spend no more than $15, so the cost of cherries (4x) plus the cost of grapes (2.5y) should be less than or equal to $15: 4x + 2.5y ≤ 15
2. We need at least 5 lb in total, so the sum of cherries and grapes (x + y) needs to be greater than or equal to 5: x + y ≥ 5
We will solve this system of inequalities to find the feasible region representing the amount of each fruit we can buy.
1. Graph the equation 4x + 2.5y = 15:
- Rearrange the equation to y = (-4/2.5)x + 6:
y = (-8/5)x + 6
- Plot two points on the line: (0, 6) and (3.75, 0).
2. Graph the equation x + y = 5:
- Solve for y: y = 5 - x
- Plot two points on the line: (0, 5) and (5, 0).
3. Shade the area below the line y = (-8/5)x + 6 and above the line y = 5 - x, as this represents the feasible region.
The final graph will show the feasible region where the amount of cherries (x) and grapes (y) that can be bought satisfies the given conditions.