Mo has $90.00 already saved and has a job making $8.00 per hour. Merv already has $50.00 saved and has a job making $8.50 per hour. They both want to save enough money to buy a pair of airpods for $130.00. Who reaches their financial goal first?
Task 1 - Analyze Mo’s Story
Write Mo’s financial situation expressing their total dollar amount saved as a linear function of time (hours) in Slope Intercept Form. In a few sentences interpret what the slope represents in this situation. Interpret what the y-intercept means in terms of Mo’s financial story.
Task 2 - Analyze Merv’s Story
Write Merv’s financial situation expressing their total dollar amount saved as a linear function of time (hours) in Slope Intercept Form. In a few sentences interpret what the slope represents in this situation. Interpret what the y-intercept means in terms of Merv’s financial story.
Task 3 - Evaluate and Compare
Calculate who will reach their financial goal of purchasing the airpods if they both work 8 hours this week. Provide a full Algebraic solution and a paragraph explaining your reasoning.
Mo: 8.00x + 90
Merv: 8.50x + 50
See what you can do with that.
Hey oobleck thank you but they must be explained in sentences.
Task 1 - Analyze Mo’s Story:
Mo's total dollar amount saved can be expressed as a linear function of time (hours) in Slope Intercept Form. Let's define the variables:
- x: time in hours
- y: total dollar amount saved by Mo
Based on the information provided, Mo already has $90.00 saved and is earning $8.00 per hour. The equation representing Mo's financial situation in Slope Intercept Form is:
y = 8x + 90
In this equation, the slope represents the rate of increase in Mo's savings. It shows that for every hour worked, Mo saves an additional $8.00. The y-intercept (90) represents Mo's initial savings before he started working.
Task 2 - Analyze Merv’s Story:
Merv's total dollar amount saved can also be expressed as a linear function of time (hours) in Slope Intercept Form. Again, let's define the variables:
- x: time in hours
- y: total dollar amount saved by Merv
According to the information given, Merv already has $50.00 saved and is earning $8.50 per hour. The equation representing Merv's financial situation in Slope Intercept Form is:
y = 8.5x + 50
In this equation, the slope indicates the rate of increase in Merv's savings. It shows that for every hour worked, Merv saves an additional $8.50. The y-intercept (50) represents Merv's initial savings before he started working.
Task 3 - Evaluate and Compare:
To determine who will reach their financial goal first, we need to calculate the number of hours it will take for each person to save enough money to buy the Airpods.
For Mo, we can substitute x = 8 (as he is working 8 hours) into his equation:
y = 8 * 8 + 90
y = 64 + 90
y = 154
Therefore, Mo will have $154.00 after working 8 hours.
For Merv, we can substitute x = 8 into his equation:
y = 8.5 * 8 + 50
y = 68 + 50
y = 118
Therefore, Merv will have $118.00 after working 8 hours.
Comparing the results, we can see that Mo will reach his financial goal first, as he will have $154.00 after working 8 hours, while Merv will only have $118.00.
Task 1 - Analyze Mo's Story:
To express Mo's financial situation as a linear function of time in slope-intercept form, we'll use the equation y = mx + b, where y represents the total dollar amount saved, x represents the time in hours, m represents the hourly wage, and b represents the initial amount already saved.
In this case, Mo has $90.00 already saved and earns $8.00 per hour. So, Mo's linear function would be:
y = 8x + 90
The slope (m) in this situation represents the hourly wage of $8.00 per hour. It tells us that for every hour worked, Mo will earn an additional $8.00.
The y-intercept (b) represents the initial amount already saved by Mo, which is $90.00. This means that Mo had $90.00 even before starting their job.
Task 2 - Analyze Merv's Story:
Similarly, to express Merv's financial situation as a linear function of time in slope-intercept form, we'll use the same equation y = mx + b.
Merv has $50.00 saved already and earns $8.50 per hour. So, Merv's linear function would be:
y = 8.50x + 50
Again, the slope (m) represents the hourly wage of $8.50 per hour. It tells us that for every hour worked, Merv will earn an additional $8.50.
The y-intercept (b) represents the initial amount already saved by Merv, which is $50.00. This means that Merv had $50.00 even before starting their job.
Task 3 - Evaluate and Compare:
To calculate who will reach their financial goal first, we need to find out the time (in hours) it takes for each person to reach $130.00.
For Mo:
y = 8x + 90
Setting y = $130.00:
130 = 8x + 90
Simplifying the equation:
8x = 40
x = 5
So, Mo will take 5 hours to reach $130.00.
For Merv:
y = 8.50x + 50
Setting y = $130.00:
130 = 8.50x + 50
Simplifying the equation:
8.50x = 80
x = 9.41
So, Merv will take approximately 9.41 hours to reach $130.00.
Comparing the times, we see that Mo will reach their financial goal first since they will take 5 hours, whereas Merv will take approximately 9.41 hours.