Ask a New Question
Menu

Use the graph, table and equation to answer the question.

Andrew, Mai and Shakira are competing to see who can save the most money in one month.
Mais savings:
number of days:5,10,15,20
amount saved:17,24,31,38
Shakira's saving: y-20=3(x-5)
Andres saving: its a chart where the line starts at (0,3) and ends at (4,11)

Who started with the smallest savings? What was the amount? You must show ALL work to earn full credit.

9 answers

To determine who started with the smallest savings among Andrew, Mai, and Shakira, let's analyze the savings data we're provided for each person.

Mai's Savings:

We have a table for Mai's savings, which shows the number of days and the amount saved:

  • Day 5: $17
  • Day 10: $24
  • Day 15: $31
  • Day 20: $38

Let's find the savings for the initial day (Day 0). Since the data starts from day 5, we can assume a linear relationship and compute the values at Day 0.

To find the slope \(m\) of Mai's savings from the points (5, 17) and (10, 24):

Step 1: Calculate the slope of Mai's savings

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{24 - 17}{10 - 5} = \frac{7}{5} = 1.4 \]

Step 2: Find the y-intercept using the point (5, 17)

Using the slope-intercept form \(y = mx + b\): \[ 17 = 1.4 \cdot 5 + b \] \[ 17 = 7 + b \implies b = 17 - 7 = 10 \]

So, Mai's savings equation is: \[ y = 1.4x + 10 \]

Step 3: Calculate savings at Day 0

Plugging in \(x=0\): \[ y = 1.4 \cdot 0 + 10 = 10 \] Thus, Mai started with $10 in savings.

Shakira's Savings:

Shakira's savings are given by the equation \(y - 20 = 3(x - 5)\).

Step 1: Rearranging into slope-intercept form

\[ y - 20 = 3x - 15 \implies y = 3x + 5 \]

Step 2: Calculate savings at Day 0

Plugging in \(x=0\): \[ y = 3 \cdot 0 + 5 = 5 \] Thus, Shakira started with $5 in savings.

Andrew's Savings:

Andrew's savings are given as a chart starting from point (0, 3) and ending at (4, 11).

From the point (0, 3), it is clear that Andrew started with $3 in savings.

Conclusion:

Now let's summarize the initial savings for each participant:

  • Mai: $10
  • Shakira: $5
  • Andrew: $3

Answer: Andrew started with the smallest savings, which was $3.

can u show me like what to write down? this is too confusing please and thank you

Sure! Below is a step-by-step breakdown of the work you can write down to explain how to determine who started with the smallest savings.

Title: Who Started with the Smallest Savings?

1. Mai's Savings:

  • Savings Data:

    • Day 5: $17
    • Day 10: $24
    • Day 15: $31
    • Day 20: $38

  • Finding the Savings at Day 0:
    We need to find the initial savings when Day = 0.

    • Calculate the slope \(m\) between two points:
      Points (5, 17) and (10, 24):
      \( m = \frac{24 - 17}{10 - 5} = \frac{7}{5} = 1.4 \)

  • Finding the y-intercept (initial savings):
    Using the slope-intercept form \(y = mx + b\):
    Take the point (5, 17):
    \[ 17 = 1.4(5) + b
    \]
    \[ 17 = 7 + b \implies b = 17 - 7 = 10
    \]
    Thus, Mai's savings equation is:
    \[ y = 1.4x + 10 \]

  • Savings at Day 0:
    \[ y = 1.4(0) + 10 = 10
    \]
    So, Mai started with $10.

2. Shakira's Savings:

  • Savings Equation:
    \( y - 20 = 3(x - 5) \)

  • Rearranging to Slope-Intercept Form:
    \[ y - 20 = 3x - 15
    \]
    \[ y = 3x + 5
    \]

  • Finding Savings at Day 0:
    \[ y = 3(0) + 5 = 5
    \]
    So, Shakira started with $5.

3. Andrew's Savings:

  • Savings Start Point:
    Andrew's savings starts at (0, 3), so he started with $3.

4. Summary of Initial Savings:

  • Mai's Initial Savings: $10
  • Shakira's Initial Savings: $5
  • Andrew's Initial Savings: $3

5. Conclusion:

Andrew started with the smallest savings, which was $3.

Feel free to copy and write this structured response for clarity!

I don't wanna type all that, just number

Understood! Here’s a concise numbered list you can write down without all the explanations:

1. Mai's Savings Calculation:

  • Savings Data: (5, 17), (10, 24), (15, 31), (20, 38)
  • Slope \(m = \frac{7}{5} = 1.4\)
  • Savings Equation: \(y = 1.4x + 10\)
  • Savings at Day 0: \(y = 10\)

2. Shakira's Savings Calculation:

  • Savings Equation: \(y - 20 = 3(x - 5)\)
  • Rearranged: \(y = 3x + 5\)
  • Savings at Day 0: \(y = 5\)

3. Andrew's Savings:

  • Starts from (0, 3): Initial Savings = $3

4. Summary of Initial Savings:

  • Mai: $10
  • Shakira: $5
  • Andrew: $3

5. Conclusion:

  • Andrew started with the smallest savings ($3).

You can just copy this list to your notes!

same thing but dif question
Who is saving the least amount of money per day? What is the amount? You must show ALL work to earn full credit.

Sure! Below is a concise numbered list to answer the question about who is saving the least amount of money per day, along with the necessary calculations.

1. Mai's Savings Calculation:

  • Savings Data: (5, 17), (10, 24), (15, 31), (20, 38)
  • Finding the Amount Saved Per Day:
    • Days 5 to 10: \( \frac{24 - 17}{10 - 5} = \frac{7}{5} = 1.4\)
    • Days 10 to 15: \( \frac{31 - 24}{15 - 10} = \frac{7}{5} = 1.4\)
    • Days 15 to 20: \( \frac{38 - 31}{20 - 15} = \frac{7}{5} = 1.4\)
  • Average Amount Saved Per Day: 1.4

2. Shakira's Savings Calculation:

  • Savings Equation: \(y - 20 = 3(x - 5)\) → Rearranged: \(y = 3x + 5\)
  • Finding the Amount Saved Per Day:
    • The slope (rate of saving) is 3, so she saves $3 per day.

3. Andrew's Savings Calculation:

  • Points: (0, 3) to (4, 11)
  • Calculating Savings per Day:
    • Amount Saved: \(11 - 3 = 8\)
    • Number of Days: \(4 - 0 = 4\)
    • Amount Saved Per Day: \( \frac{8}{4} = 2\)

4. Summary of Daily Savings:

  • Mai: $1.4 per day
  • Shakira: $3 per day
  • Andrew: $2 per day

5. Conclusion:

  • Mai is saving the least amount of money per day, which is $1.4.

You can copy this structured list to your notes!

Who will have the most money on day 30? How much money will the person have? You must show ALL work to earn full credit.

Certainly! Below is a concise numbered list to determine who will have the most money on day 30, along with the necessary calculations for each person.

1. Mai's Savings Calculation:

  • Savings Equation: \(y = 1.4x + 10\)
  • Calculating Savings on Day 30: \[ y = 1.4(30) + 10 \] \[ y = 42 + 10 = 52 \]
  • Mai's Total Savings on Day 30: $52

2. Shakira's Savings Calculation:

  • Savings Equation: \(y = 3x + 5\)
  • Calculating Savings on Day 30: \[ y = 3(30) + 5 \] \[ y = 90 + 5 = 95 \]
  • Shakira's Total Savings on Day 30: $95

3. Andrew's Savings Calculation:

  • Finding the Savings Equation:
    • From (0, 3) to (4, 11), the slope is: \[ \text{Slope} = \frac{11 - 3}{4 - 0} = \frac{8}{4} = 2 \]
  • Savings Equation: \(y = 2x + 3\)
  • Calculating Savings on Day 30: \[ y = 2(30) + 3 \] \[ y = 60 + 3 = 63 \]
  • Andrew's Total Savings on Day 30: $63

4. Summary of Total Savings on Day 30:

  • Mai: $52
  • Shakira: $95
  • Andrew: $63

5. Conclusion:

  • Shakira will have the most money on Day 30, which will be $95.

You can copy this structured response to your notes!