Suppose you are saving money for a new cell phone. At week 0 you have $20 and at week 10 you have $100. If y represents the amount of money you have saved and x represents
one-eighth; $8 is put away each week.
10; $10 is put away each week.
8; $8 is put away each week.
one-tenth; $10 is put away each week.
In this scenario, x represents the number of weeks and y represents the amount of money saved.
As given, at week 0, you have $20. This means y = $20 when x = 0.
At week 10, you have $100. This means y = $100 when x = 10.
Since $8 is put away each week, the amount saved can be represented by the equation: y = 8x + 20.
Thus, the correct answer is "8; $8 is put away each week."
To determine the amount of money saved each week, you can set up a linear equation in the form y = mx + b, where y represents the amount of money saved and x represents the number of weeks.
Given:
- At week 0, you have $20. Therefore, the initial savings (b) is $20.
- At week 10, you have $100. Therefore, the final savings (y) is $100.
- $8 is put away each week.
Now, let's substitute the values into the equation and solve for the missing variable (slope, m):
y = mx + b
$100 = m(10) + $20
$100 = 10m + $20
$100 - $20 = 10m
$80 = 10m
To calculate the value of m (the slope), divide both sides by 10:
$80 / 10 = 10m / 10
$8 = m
Therefore, the amount of money saved each week is $8.
To find the equation that represents the amount of money you have saved, you need to determine the rate at which you are saving money. In this case, you are putting away $8 each week.
Since you start with $20, the starting point (when x = 0) is 20 dollars. To find the equation, you can use the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
The slope, in this case, represents the rate at which you are saving money, which is $8 per week. Since x represents one-eighth, you can divide x by 1/8 to get the number of weeks.
So, the equation is y = 8 * (1/8)x + 20.
To find out how much money you will have at week 10, you can substitute x = 10 into the equation:
y = 8 * (1/8) * 10 + 20
= 10 + 20
= 30.
Therefore, at week 10, you will have $30 saved up for your new cell phone.