John is at a local bait shop; he wants to buy bait for his fishing trip. At the store, they are selling live bait for $12 a pound and natural bait for $7 a pound. John would like to get at least 3 pounds of live bait, but he only has a budget of $63. Let x be the amount of live bait and y be the amount of natural bait. Model the scenario with a system of inequalities.
Using your definitions ...
"at least 3 pounds of live bait" -----> x ≥ 3
"only has a budget of $63" ----> 12x + 7y ≤ 63
To model the scenario with a system of inequalities, we need to set up the constraints for John's budget and the amount of live bait he wants to purchase.
Let's write the system of inequalities:
Constraint 1: John wants at least 3 pounds of live bait.
x ≥ 3
Constraint 2: John's budget is $63.
12x + 7y ≤ 63
So, the system of inequalities is:
x ≥ 3
12x + 7y ≤ 63
To model the scenario with a system of inequalities, let's define the variables and establish the constraints:
Let x be the amount of live bait (in pounds).
Let y be the amount of natural bait (in pounds).
Now, let's establish the constraints based on the given information:
1. John wants at least 3 pounds of live bait:
x ≥ 3
2. John's budget is $63:
12x + 7y ≤ 63
To summarize, the system of inequalities representing the scenario is:
x ≥ 3
12x + 7y ≤ 63
These inequalities represent the minimum weight requirement for live bait (x ≥ 3) and the budget constraint (12x + 7y ≤ 63).