Question

on the first day of a semester, a film club has 90 members. each day after the first day of the semester, 10 new members join the film club. if no members leave the film club, how many total members will the film club have 4 days after the first day of the semester?
a) 400
b) 130
c) 94
d) 90

Explanation:

Step1: Identify the initial number and daily increase

Initial members: \( 90 \), daily new members: \( 1 \) (wait, no, wait—the problem says "10 new members"? Wait, no, looking at the text again: "10 new members"? Wait, the OCR might be off. Wait, the options: A) 130? Wait, no, let's re-express. Wait, the problem: "On the first day of a semester, a film club has 90 members. Each day after the first day of the semester, 10 new members join the film club. If no members leave the film club, how many total members will the film club have 4 days after the first day of the semester?" Wait, maybe the OCR had a typo. Let's assume: initial = 90, daily increase = 10, days after first day: 4 days. So total members after 4 days: initial + (daily increase number of days). Wait, no: first day: 90. Then day 1 after first: 90 +10, day 2: 90 +102, day 3: 90 +103, day 4: 90 +104? Wait, no—wait, "4 days after the first day" means days 1,2,3,4 after the first day. So total days of adding: 4 days. So total members = 90 + 104? Wait, no, wait: first day: 90. Then each day after (so day 1 after first: 90 +10, day 2 after: 90 +102, day 3 after: 90 +103, day 4 after: 90 +104? Wait, 90 + 40 = 130? Wait, option B is 130. Wait, let's check:

Initial: 90 (first day)

Day 1 after first: 90 +10 = 100

Day 2 after first: 100 +10 = 110

Day 3 after first: 110 +10 = 120

Day 4 after first: 120 +10 = 130

Yes, so the calculation is 90 + 10*4 = 90 +40 = 130.

Step1: Calculate total new members in 4 days

Daily new members: \( 10 \), number of days: \( 4 \). So total new members: \( 10 \times 4 = 40 \)

Step2: Add to initial members

Initial members: \( 90 \). Total members: \( 90 + 40 = 130 \)

Answer:

B) 130