Question

The principal of a school is hosting a small luncheon for her staff. She plans to prepare two sandwiches for each person. Some staff members offer to bring salads and beverages.
The principal has a budget of $225 and expects at least 16 people to attend. Sandwiches cost $3 each.



Select all of the equations and inequalities that could represent the constraints in the situation, where n is the number of people attending and s is the number of sandwiches.



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Select all that apply:
A. n ≥ 16
B. n ≥ 32
C. s < 32
D. s = 2n
E. 3n ≤ 225
F. 3s ≤ 225

Answer 1

The constraints in the question are given by the definition of the variables;

The constraints are represented by the following equation and inequalities.

• A. n ≥ 16

• D. s = 2·n

• F. 3s ≤ 225

Reasons:

The budget of the principal = $225

Number of people expected = 16 people

Number of sandwich per person = 2

Cost of each sandwich = $3

Required:

To select the inequalities that represent the situation's constraint

Solution:

The variable that represent the number of people attending = n

The number of sandwiches = s

From the question , we have;

The number of sandwich per attendee = 2 sandwiches

The total number of sandwich, s, for n attendees = 2·n

Therefore, we have;

s = 2·n

The number of people attending is at least 16, therefore;

n ≥ 16

The cost of the s sandwich = $3 × s

The total cost should be less than or equal to given budget of $225,

therefore;

3s ≤ 225

The equations and inequalities that could represent the constraints are;

A. n ≥ 16, D. s = 2·n, and F. 3s ≤ 225

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