Question
John is saving up to buy a bike. He already has $115 and makes $25 for every lawn that he mows. John’s savings can be modeled by the equation s=25m+115
𝑠
=
25
𝑚
+
115
, in which s is the amount of John’s savings (in dollars) and m is the number of lawns he has mowed. What is the dependent variable for the inverse of the given equation?(1
𝑠
=
25
𝑚
+
115
, in which s is the amount of John’s savings (in dollars) and m is the number of lawns he has mowed. What is the dependent variable for the inverse of the given equation?(1
Answers
GPT-4o mini
In the equation \( s = 25m + 115 \), \( s \) represents John's savings, which is the dependent variable, and \( m \) represents the number of lawns he has mowed, which is the independent variable.
To find the inverse of the equation, we need to solve for \( m \) in terms of \( s \):
1. Start with the original equation:
\[ s = 25m + 115 \]
2. Subtract 115 from both sides:
\[ s - 115 = 25m \]
3. Divide both sides by 25:
\[ m = \frac{s - 115}{25} \]
In the inverse equation \( m = \frac{s - 115}{25} \), the dependent variable is now \( m \) (the number of lawns mowed), and \( s \) (the amount of savings) is the independent variable.
Therefore, the dependent variable for the inverse of the given equation is \( m \).
To find the inverse of the equation, we need to solve for \( m \) in terms of \( s \):
1. Start with the original equation:
\[ s = 25m + 115 \]
2. Subtract 115 from both sides:
\[ s - 115 = 25m \]
3. Divide both sides by 25:
\[ m = \frac{s - 115}{25} \]
In the inverse equation \( m = \frac{s - 115}{25} \), the dependent variable is now \( m \) (the number of lawns mowed), and \( s \) (the amount of savings) is the independent variable.
Therefore, the dependent variable for the inverse of the given equation is \( m \).