Question

Meha is helping her aunt plan a birthday party for her cousin at the science center. Her aunt tells her that the party will cost $100, plus $3.50 per child and $8.50 per adult. There needs to be at least adult and at least two children at the party. She has budgeted $250 for the party and that is the maximum amount she wants to spend.

Write a two-variable inequality to represent this situation. Be sure to define the variables you use in your inequality.

Let x = the number of children at the party
Let y = the number of adults at the party.

____x + ____y + ____ ____ ____
(Options: 3.50, 5, 8.50, 12, 100, 250, 500, < > ≤ ≥)


Is it possible for the party to include 10 children and 20 adults? Use your inequality from part A to check.

(Dropdown 1: Yes, no) because (Dropdown 2: when 10 and 20 are substitute into the equation you get 205 which is less than 250, when 10 and 20 are substitute into the equation you get 255 which is greater than 250, when 10 and 20 are substitute into the equation you get 155 which is less than 250, when 10 and 20 are substitute into the equation you get 305 which is greater than 250)


State if the following points are viable solutions to the problem (remember to take in the constraints)

3, 2 (yes or no)
-10, 0 (yes or no)
30, 10 (yes or no)
15, 5 (yes or no)
10, -5 (yes or no)

Answer 1

Let x = number of children and y = number of adults.

Cost inequality: 3.50x + 8.50y + 100 ≤ 250

(Also require x ≥ 2 and y ≥ 1.)

Is 10 children and 20 adults possible? No, because when 10 and 20 are substituted into the inequality you get 305 which is greater than 250.

Viability of points (must satisfy x ≥ 2, y ≥ 1, and cost ≤ 250):
- (3, 2): yes (cost = 127.50)
- (-10, 0): no (violates x ≥ 2 and y ≥ 1)
- (30, 10): no (cost = 290 > 250)
- (15, 5): yes (cost = 195)
- (10, -5): no (violates y ≥ 1)