In order to make a profit, a zoo needs to sell at least 350 admission tickets each day. Four student groups, each of which includes 48 students, have purchased tickets for admission. If z represents the number of additional tickets sold today, and the zoo made its daily profit goal, which of the following inequalities could represent all possible values for z ?
A. 4(48) + z ≤ 350
B. 4(48) + z ≥ 350
C. 4(48) - z ≤ 350
D. 4(48) - z ≥ 350
Answer:B
In order to make a profit, a zoo needs to sell at least 350 admission tickets each day. Four student groups, each of which includes 48 students, have purchased tickets for admission. If z represents the number of additional tickets sold today, and the zoo made its daily profit goal, which of the following inequalities could represent all possible values for z ?
A. 4(48) + z ≤ 350 B. 4(48) + z ≥ 350 C. 4(48) - z ≤ 350 D. 4(48) - z ≥ 350
Explanation: B So far the zoo has sold 4 × 48 = 192 tickets. To make a profit, the zoo will need to sell at least 350 - 192 = 158 additional tickets. So, z needs to be at least 158. Calculate z in each of the answers to see which gives you a value of z ≥ 158. In (A), z ≤ 350 - 4(48), so z ≤ 158. Eliminate (A). Choice (B) gives you z ≥ 158. Keep (B). Choice (C) gives you z ≥ -158. Eliminate (C). Choice (D) gives you z ≤ -158. Eliminate (D). Choice (B) is the correct answer.