The students at Vienna Elementary sold donuts everyday at school for 6 months. The table below shows the earnings for the first 6 weeks. If the pattern continues, how long will it take the students to earn more than $1,000 total? Week Number Amount Earned 1 $110 2 $100 3 $90 4 $110 5 $100 6 $90 (1 point) Responses 6 weeks 6 weeks 8 weeks 8 weeks 9 weeks 9 weeks 10 weeks 10 weeks Skip to navigation

Answer 1

To determine how long it will take the students to earn more than $1,000, we first need to analyze the earnings over the first 6 weeks to identify the pattern.

From the table, the amounts earned each week are as follows:

• Week 1: $110
• Week 2: $100
• Week 3: $90
• Week 4: $110
• Week 5: $100
• Week 6: $90

If we look closely, we can see a repeating pattern in the earnings every 3 weeks:

• Weeks 1-3: $110, $100, $90 → Total for 3 weeks = $110 + $100 + $90 = $300
• Weeks 4-6: $110, $100, $90 → Total for another 3 weeks = $110 + $100 + $90 = $300

Thus, every 3 weeks, the students earn a total of $300.

Next, we calculate how many times this pattern needs to repeat in order to exceed $1,000:

1. Total earnings after 3 weeks: $300
2. After 6 weeks: $600 (2 cycles of 3 weeks)
3. After 9 weeks: $900 (3 cycles of 3 weeks)

At 9 weeks, the students have earned $900, which is still less than $1,000.

Now, we can see what happens in the 10th week:

• In week 10 (the first week of the next cycle), they would earn $110.

So after 10 weeks:

• Total earnings = $900 (after 9 weeks) + $110 (week 10) = $1,010

Now, they have surpassed $1,000. Thus, it takes 10 weeks for the students to earn more than $1,000.

The answer is 10 weeks.