David is planning a dinner for his birthday. At one restaurant, the cost per person for dinner is $15, with an additional one-time set-up charge of $35. David has a maximum budget of $150. If p represents the number of people (including David) who will attend the dinner, which of the following inequalities represents the number of people who can attend within budget?
A. 15p ≤ 150 + 35
B. 35 ≤ 150 - 15p
C. 15p ≥ 150 - 35
D. 35 ≥ 150 - 15p
Answer:B
David is planning a dinner for his birthday. At one restaurant, the cost per person for dinner is $15, with an additional one-time set-up charge of $35. David has a maximum budget of $150. If p represents the number of people (including David) who will attend the dinner, which of the following inequalities represents the number of people who can attend within budget?
A. 15p ≤ 150 + 35 B. 35 ≤ 150 - 15p C. 15p ≥ 150 - 35 D. 35 ≥ 150 - 15p
Explanation: B Subtract the one-time set-up charge from David's budget first: 150 - 35 = 115. Calculate the number of people David can invite as follows: 115 ÷ 15 = 7.6. David can invite at most 7 people (including himself), so p ≤ 7. In (A), 15p ≤ 185, so p ≤ 12.3 or p ≤ 12.3. Eliminate (A). Solve for p in (B) as follows: add 15p to both sides to get 15p + 35 ≤ 150, so 15p ≤ 115 and p ≤ 7.6. The correct answer is (B).