QuestionJose wants to spend no more than on apples and grapes for the month. Apples cost per pound, and grapes cost per pound. Jose also wants his monthly caloric intake from apples and grapes to be greater than 2,000 calories. He determines that 1 pound of apples has 200 calories and 1 pound of grapes has 300 calories. Let a represent the number of pounds of apples and represent the number of pounds of grapes.
Which system of inequalities can be used to determine the number of pounds of apples and the number of pounds of grapes that Jose can buy for a month?
(a)
(b)
(C)
(d)
Studdy Solution
STEP 1
1. Jose has a budget constraint of no more than 1.50 per pound, and grapes cost $2 per pound.
3. Jose wants his caloric intake from apples and grapes to be greater than 2,000 calories.
4. 1 pound of apples provides 200 calories, and 1 pound of grapes provides 300 calories.
5. Let \( a \) represent the number of pounds of apples and \( g \) represent the number of pounds of grapes.
STEP 2
1. Formulate the inequality for the cost constraint.
2. Formulate the inequality for the caloric intake constraint.
3. Identify the correct system of inequalities from the given options.
STEP 3
The cost constraint is given by the total amount Jose can spend on apples and grapes. The cost of apples is 2 per pound. Therefore, the inequality representing the cost constraint is:
STEP 4
The caloric intake constraint requires that Jose's intake from apples and grapes be greater than 2,000 calories. Since apples provide 200 calories per pound and grapes provide 300 calories per pound, the inequality representing the caloric intake constraint is:
STEP 5
Combine the inequalities derived from the cost and caloric intake constraints to form the system of inequalities. The correct system of inequalities is:
This corresponds to option (b).
The correct system of inequalities is:
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