All of the inequalities that could represent this situation and graph include the following;
A. 2(c + 1) - 50 ≥ 352
B. 310 + c ≤ 3(c - 30)
Next, we would evaluate and solve each of the inequality in order to determine the solutions that matches the graph (number line);
2(c + 1) - 50 ≥ 352
2(c + 1) - 50 - 352 ≥ 352 - 352
2(c + 1) - 402 ≥ 0
2c + 2 - 402 ≥ 0
2c - 400 ≥ 0
2c ≥ 400
c ≥ 200 (Correct inequality)
310 + c ≤ 3(c - 30)
310 + c ≤ 3c - 90
310 + 90 ≤ 3c - c
400 ≤ 2c
c ≥ 200 (Correct inequality)
20(c - 1) ≥ 4000
c - 1 ≥ 200
c ≥ 200 + 1
c ≥ 201 (Inorrect inequality)
5(c + 1) - 200 ≥ 250
5(c + 1) ≥ 250 + 200
5(c + 1) ≥ 450
c + 1 ≥ 90
c ≥ 89 (Inorrect inequality)
50(c - 5) ≥ 200
c - 5 ≥ 4
c ≥ 5 + 4
c ≥ 9 (Inorrect inequality)
Complete Question:
The science club is planning a car wash fundraiser. Halona writes and graphs an inequality to represent the number of cars, C, the science club needs to wash to make a profit.
Select all of the the inequalities that could represent this situation and graph.
2(c + 1) - 50 ≥ 352
310 + c ≤ 3(c - 30)
20(c - 1) ≥ 4000
5(c + 1) - 200 ≥ 250
50(c - 5) ≥ 200