Question
Writing Solve StartFraction y Over 12 EndFraction
minus6equals5. Use pencil and paper. Think of a situation in your own life that could be represented by a two-step equation. Write and solve the two-step equation.
Question content area bottom
Part 1
yequals
enter your response here
(Type an integer or a simplified fraction.)
minus6equals5. Use pencil and paper. Think of a situation in your own life that could be represented by a two-step equation. Write and solve the two-step equation.
Question content area bottom
Part 1
yequals
enter your response here
(Type an integer or a simplified fraction.)
Answers
GPT-4o mini
To solve the equation given \( \frac{y}{12} - 6 = 5 \), we can follow these steps:
### Step 1: Isolate the fraction
First, add 6 to both sides of the equation:
\[
\frac{y}{12} - 6 + 6 = 5 + 6
\]
This simplifies to:
\[
\frac{y}{12} = 11
\]
### Step 2: Solve for \( y \)
Now, to eliminate the fraction, multiply both sides of the equation by 12:
\[
12 \cdot \frac{y}{12} = 11 \cdot 12
\]
This simplifies to:
\[
y = 132
\]
So the solution is:
\[
y = 132
\]
---
### Part 2: Real-Life Situation
Let's think of a situation that could be modeled by a two-step equation. For example, you want to save money for a new bike that costs $132. You have saved $6 but are unsure how much more you need to save.
### Two-Step Equation
Let \( y \) represent the amount of money you still need to save. The equation can be set up as follows:
\[
\frac{y}{12} - 6 = 5
\]
In this scenario:
- You have \( 6 \) dollars (which we will treat as a deduction).
- The total cost of the bike is \( 132 \) dollars.
### Rewritten Two-Step Equation
After reasoning through it, the equation can be adjusted or simplified. The goal is just to find out how much more you need to save after an initial deposit of \( 6 \).
This could give you an equation similar to:
\[
y - 6 = 132 \quad \text{(if we consider just total savings)}
\]
Solving for \( y \):
\[
y = 132 + 6 \Rightarrow y = 138
\]
Thus, if you want to save a total of \( 132 \) dollars, and you have already saved \( 6 \) dollars, you need to save \( 132 - 6 = 126 \) more.
The equation nicely captures the situation you are experiencing.
### Step 1: Isolate the fraction
First, add 6 to both sides of the equation:
\[
\frac{y}{12} - 6 + 6 = 5 + 6
\]
This simplifies to:
\[
\frac{y}{12} = 11
\]
### Step 2: Solve for \( y \)
Now, to eliminate the fraction, multiply both sides of the equation by 12:
\[
12 \cdot \frac{y}{12} = 11 \cdot 12
\]
This simplifies to:
\[
y = 132
\]
So the solution is:
\[
y = 132
\]
---
### Part 2: Real-Life Situation
Let's think of a situation that could be modeled by a two-step equation. For example, you want to save money for a new bike that costs $132. You have saved $6 but are unsure how much more you need to save.
### Two-Step Equation
Let \( y \) represent the amount of money you still need to save. The equation can be set up as follows:
\[
\frac{y}{12} - 6 = 5
\]
In this scenario:
- You have \( 6 \) dollars (which we will treat as a deduction).
- The total cost of the bike is \( 132 \) dollars.
### Rewritten Two-Step Equation
After reasoning through it, the equation can be adjusted or simplified. The goal is just to find out how much more you need to save after an initial deposit of \( 6 \).
This could give you an equation similar to:
\[
y - 6 = 132 \quad \text{(if we consider just total savings)}
\]
Solving for \( y \):
\[
y = 132 + 6 \Rightarrow y = 138
\]
Thus, if you want to save a total of \( 132 \) dollars, and you have already saved \( 6 \) dollars, you need to save \( 132 - 6 = 126 \) more.
The equation nicely captures the situation you are experiencing.