Question

1. each week, alexas company deducts money from her paycheck and places it into a savings account. she saves $75.50 each week. how many weeks will it take to save $528.50?

1. the average length of five bean seedlings is 7.3 cm. refer to the table and determine the missing seedlings length. show your work.

length in cm

5.3

8.2

9.1

6.4

?

Explanation:

Problem 9

Step1: Define the problem

We know the weekly savings (\( \$75.50 \)) and the total amount to save (\( \$528.50 \)). We need to find the number of weeks (\( n \)) such that \( 75.50 \times n = 528.50 \).

Step2: Solve for \( n \)

To find \( n \), we divide the total amount by the weekly savings: \( n=\frac{528.50}{75.50} \).

Step3: Calculate the division

\( \frac{528.50}{75.50} = 7 \) (since \( 75.50\times7 = 528.50 \)).

Step1: Recall the formula for average

The average (\( \bar{x} \)) of a set of numbers is the sum of the numbers (\( \sum x \)) divided by the number of numbers (\( n \)): \( \bar{x}=\frac{\sum x}{n} \). Here, \( \bar{x} = 7.3 \), \( n = 5 \), and we know four of the five numbers. Let the missing number be \( x \).

Step2: Write the sum equation

The sum of the five numbers is \( 5.3 + 8.2 + 9.1 + 6.4 + x \). The average is \( 7.3 \), so:

$$ 7.3=\frac{5.3 + 8.2 + 9.1 + 6.4 + x}{5} $$

Step3: Multiply both sides by 5

$$ 7.3\times5=5.3 + 8.2 + 9.1 + 6.4 + x $$

\( 36.5=5.3 + 8.2 + 9.1 + 6.4 + x \)

Step4: Calculate the sum of known numbers

\( 5.3 + 8.2 + 9.1 + 6.4 = 29 \)

Step5: Solve for \( x \)

\( 36.5=29 + x \)
Subtract 29 from both sides: \( x = 36.5 - 29 = 7.5 \)

Answer:

It will take 7 weeks.

Problem 10