Joe is saving money. He starts with $85 and saves $15 per week.
a) write a linear equation to model this example.
b) how many weeks will it take for joe to have $370 in savings?
a) The linear equation that models this example can be written as:
savings = $85 + $15 * weeks
b) To find the number of weeks it will take for Joe to have $370 in savings, we can set up the equation:
$370 = $85 + $15 * weeks
Now, we can solve for weeks:
$370 - $85 = $15 * weeks
$285 = $15 * weeks
Divide both sides of the equation by $15:
$285/$15 = weeks
19 = weeks
Therefore, it will take Joe 19 weeks to have $370 in savings.
a) To write a linear equation to model Joe's savings, we need to identify the variables involved and their relationship. In this case, the amount Joe saves each week is directly proportional to the number of weeks he has been saving.
Let's represent the number of weeks as 'w' and the amount of money he has saved as 's'. Since Joe starts with $85, we can consider this as the initial amount. Joe saves $15 each week, so we can say that the amount saved after 'w' weeks can be calculated as:
s = 15w + 85
This equation represents Joe's savings after 'w' weeks.
b) We are given that Joe wants to have $370 in savings. We can substitute this value into the equation we derived in part (a) and solve for 'w':
370 = 15w + 85
To find the value of 'w', we need to isolate the variable by solving the equation:
370 - 85 = 15w
285 = 15w
Now, divide both sides of the equation by 15:
285/15 = w
19 = w
Therefore, it will take Joe 19 weeks to have $370 in savings.
a) To write a linear equation that models Joe's savings, we can use the slope-intercept form of a linear equation: y = mx + b, where y represents the amount of money saved, x represents the number of weeks, m represents the rate of saving per week, and b represents the initial amount.
In this case, Joe saves $15 per week, so our equation is y = 15x + 85.
b) To find out how many weeks it will take for Joe to have $370 in savings, we need to solve the equation 370 = 15x + 85 for x.
Subtracting 85 from both sides of the equation, we get:
370 - 85 = 15x
285 = 15x
Now, we divide both sides of the equation by 15:
285/15 = x
19 = x
Therefore, it will take Joe 19 weeks to have $370 in savings.