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.
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.
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