HELP PLEASE! URGENT!
Greg started with a certain number of quarters. He then decided on a number of quarters he would save each day. He added the quarters he saved to the amount with which he started.
At the end of day 2, Greg had a total of 26 quarters saved.
At the end of day 5, he had a total of 35 quarters saved.
At the end of day 8, he had a total of 44 quarters saved.
Hint: Create an x/y or t-chart and fill in the numbers with x-value representing the # of days and the y-value representing "total coins."
A. How many quarters does Greg start with (day zero)? Show or explain your work.
B. Write an equation in slope-intercept form to model the total quarters Greg has saved after x days.
C. Using the rate at which Greg is saving, explain why he can never have exactly 100 quarters saved by the end of any given day.
looks like every 3 days he gains 9 quarters
so the "slope" is 9/3 = 3
y = 3x + b
when x = 2, y = 26
26 = 3(2) + b
b = 20
y = 3x + 20
test: when x = 8, y = 3(8) + 20 = 44, which is the same as the given
to have 100 = 3x + 20
3x = 80
x = 80/3 days, which is not a whole number for days
To find the answer to these questions, let's start by creating a table to organize the given information:
| Days (x) | Total Quarters (y) |
|----------|--------------------|
| 0 | ? |
| 2 | 26 |
| 5 | 35 |
| 8 | 44 |
A. To find how many quarters Greg starts with on day zero, we need to find the missing value in our table. From the given information, we know that at the end of day 2, he had a total of 26 quarters. This means that in those 2 days, he saved a certain number of quarters.
From the table, we can see that from day 2 to day 5 (3 days), he saved an additional 9 quarters (35 - 26 = 9). Therefore, we can deduce that he saves 9 quarters every 3 days.
To find out how many quarters Greg starts with, we subtract the number of quarters he saved in 2 days from the total he had at the end of day 2. So, the number of quarters he starts with is 26 - 9 = 17.
Therefore, Greg starts with 17 quarters (on day zero).
B. To write an equation in slope-intercept form to model the total number of quarters Greg has saved after x days, we can use the information from the table.
We know that Greg starts with 17 quarters (y-intercept) and saves 9 quarters every 3 days (slope). So, the equation in slope-intercept form is:
y = (9/3)x + 17
C. The rate at which Greg is saving is 9 quarters every 3 days. This means he saves 3 quarters per day (9 quarters / 3 days). If we examine the table, we notice that the total number of quarters he has at the end of each day is always one more than a multiple of 3 (e.g., 26, 35, 44).
Since 100 is not one more than a multiple of 3, Greg can never have exactly 100 quarters saved by the end of any given day.