Question

Lieutenant James made an average of 3 arrests per week for 4 weeks. How many arrests does she need to make in the fifth week to raise her average to 4 arrests per week?

Answer 1

Lieutenant James needs to make 8 arrests in the fifth week to raise her average to 4 arrests per week.

Step-by-step explanation:

To solve this problem, we need to find the total number of arrests Lieutenant James has made in the first four weeks. We can do this by multiplying her average number of arrests per week (3) by the number of weeks (4). This gives us 3 * 4 = 12 arrests.

Next, we need to find the total number of arrests she needs to make in the fifth week to raise her average to 4 per week. To do this, we can set up an equation:

(12 + x) / 5 = 4

Where x represents the number of arrests in the fifth week. To solve this equation, we can multiply both sides by 5 and subtract 12 to isolate x:

12 + x = 4 * 5

x = 20 - 12

x = 8

Therefore, Lieutenant James needs to make 8 arrests in the fifth week to raise her average to 4 arrests per week.

Answer 2

5

Step-by-step explanation:

We want the average arrests to be 4. It can be done by calculating the average between the average arrests and arrests during the 5th week, so we get:

Avg(1,2,3,4,5) = (Avg(1,2,3,4) + A(5)) / 2

Where Avg(x) is the average of arrests in given weeks, and A(x) is the number of arrests in a given week.

Solving for A(5) => A(5) = 2*Avg(1,2,3,4,5) - Avg(1,2,3,4) = 2 * 4 - 3 = 8-3 = 5