Question

Week 1: saves $ 35 Week 2 : saves $ 10 Week 3: spends $ 20 Week 4: spends $ 5 Week 5 saves $15 Week 6: saves $10 Susan wants to go on a vacation to the beach with her friends . For six weeks she keeps track of how much money she spends and saves . For the next six weeks she plans on increasing the amount she saves by $10 and decreasing the amount she spends by $5. How will this affect the MEAN amount of money that Susan has ? A) The mean will not change . B) The mean will increase by approximately $5. ) The mean will increase by approximately $ 8. D) The mean will increase by approximately $15. E) The mean will increase by approximately $30.

Answer 1

The current mean amount that Susan saves or spends per week is $7.50. After increasing the savings by $10 and decreasing the amount she spends by $5, the new mean amount is $12.50. Therefore, the mean will increase by approximately $5.00.

To solve this, we'll follow these steps:

1. Calculate the current mean amount Susan saves or spends per week based on the given six weeks.

2. Adjust the amounts saved and spent by adding $10 to the savings and subtracting $5 from the amounts spent.

3. Calculate the new mean based on these adjusted amounts.

4. Determine the change in the mean amount.

Here's how:

Week 1: saves $35

Week 2: saves $10

Week 3: spends $20 (which can be viewed as saving -$20)

Week 4: spends $5 (which can be viewed as saving -$5)

Week 5: saves $15

Week 6: saves $10

First, we find the current mean:

`\[ \text{Current Mean} = (35 + 10 - 20 - 5 + 15 + 10)/(6) \]`

Then we adjust the values by adding $10 to the savings and subtracting $5 from the amounts spent, resulting in:

Week 1: saves $45

Week 2: saves $20

Week 3: saves -$15 (since spending $20 becomes spending $15)

Week 4: saves $0 (since spending $5 becomes spending $0)

Week 5: saves $25

Week 6: saves $20

Now, we calculate the new mean:

`\[ \text{New Mean} = (45 + 20 - 15 + 0 + 25 + 20)/(6) \]`

Lastly, we'll determine the change in the mean by subtracting the current mean from the new mean. Let's perform these calculations.

The current mean amount that Susan saves or spends per week is $7.50. After increasing the savings by $10 and decreasing the amount she spends by $5, the new mean amount is $12.50. Therefore, the mean will increase by approximately $5.00.

Answer 2

B) The mean will increase by $5

1) The first scenario has the following mean, adding all the spendings and savings:

`x=(35+10+20+5+15+10)/(6)=(95)/(6)=15.83`

2) Since for the following week there's an increase of $10 for her savings and a decrease of $ 5 we can write:

`\begin{gathered} x=((35+10)+(10+10)+(20-5)+(5-5)+(15+10)+(10+10))/(6)= \\ =(45+20+15+0+25+20)/(6)=(125)/(6)=20.83 \end{gathered}`

3) We can see that the mean changes, and examining the options we can state that:

the answer is B, the mean will increase by $5