Cherries cost $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.
Coordinates?
To create a graph showing the amount of each fruit you can buy, we will use the x-axis to represent the pounds of cherries, and the y-axis to represent the pounds of grapes.
To find the possible combinations of cherries and grapes, we can start with the cherries and calculate the maximum pounds of grapes that can be bought, keeping in mind the given constraints.
Let's assume the pounds of cherries as 'x' and calculate the remaining budget for grapes and the pounds of grapes that can be bought.
Given:
Cherries cost $4/lb.
Grapes cost $2.50/lb.
The maximum budget to spend is $15.
1. Cherries cost $4/lb, therefore the cost of cherries will be \(4x\).
2. The remaining budget for grapes will be \(15 - 4x\).
3. The maximum pounds of grapes that can be bought can be calculated by dividing the remaining budget for grapes by the cost of grapes (\(2.50\)). So, the maximum pounds of grapes can be bought \(= \frac{{15 - 4x}}{{2.50}}\).
We also need to consider that at least 5 lb of fruit should be bought. So the constraints can be defined as follows:
1. Cherries: \(x \geq 5\)
2. Grapes: \(\frac{{15 - 4x}}{{2.50}} \geq 5\)
To graphically represent these constraints, we can plot the following coordinates:
Coordinates (x, y):
(5, 5) (5, 6) (5, 7) (5, 8) (5, 9) (5, 10) (5, 11) (5, 12) (5, 13) (5, 14)
(6, 5) (6, 6) (6, 7) (6, 8) (6, 9) (6, 10) (6, 11) (6, 12) (6, 13) (6, 14)
(7, 5) (7, 6) (7, 7) (7, 8) (7, 9) (7, 10) (7, 11) (7, 12) (7, 13) (7, 14)
(8, 5) (8, 6) (8, 7) (8, 8) (8, 9) (8, 10) (8, 11) (8, 12) (8, 13) (8, 14)
(9, 5) (9, 6) (9, 7) (9, 8) (9, 9) (9, 10) (9, 11) (9, 12) (9, 13) (9, 14)
Therefore, the graph will have 50 coordinates representing possible combinations of cherries and grapes within the given constraints.