Emily wants to spend no more than $40 on peaches and strawberries for the month. Peaches cost $2.50 per pound, and strawberries cost $3 per pound. Emily also wants her monthly caloric intake from peaches and strawberries to be greater than 2,500 calories. She determines that 1 pound of peaches has 150 calories, and 1 pound of strawberries has 200 calories. Let p represent the number of pounds of peaches and s represent the number of pounds of strawberries.

Question

Which system of inequalities can be used to determine the number of pounds of peaches and the number of pounds of strawberries that Emily can buy in a month?
A.

Answer 1

To determine the system of inequalities for Emily's problem regarding her budget on peaches and strawberries along with her caloric intake requirement, we can set up the following inequalities:

Let:

• \( p \) = number of pounds of peaches
• \( s \) = number of pounds of strawberries

1. Budget Constraint: Emily wants to spend no more than $40 on peaches and strawberries.

   • The cost for peaches is $2.50 per pound, and for strawberries, it is $3 per pound. This gives us the inequality: \[ 2.50p + 3s \leq 40 \]

2. Caloric Intake Requirement: Emily wants her monthly caloric intake from peaches and strawberries to be greater than 2,500 calories.

   • The caloric intake from peaches is 150 calories per pound, and from strawberries, it is 200 calories per pound. This gives us the inequality: \[ 150p + 200s > 2500 \]

3. Non-negativity Constraints: Since Emily cannot buy a negative amount of fruit, we also have: \[ p \geq 0 \] \[ s \geq 0 \]

Therefore, the complete system of inequalities that represents the constraints on Emily's purchase of peaches and strawberries is:

\[ \begin{align*}

1. & \quad 2.50p + 3s \leq 40 \
2. & \quad 150p + 200s > 2500 \
3. & \quad p \geq 0 \
4. & \quad s \geq 0 \end{align*} \]