Write a real life situation to fit the following equation. Then, solve the equation In two different ways. Show all the steps. Finally, choose which solution method you liked best and explain your reason.

Real Life Situation

Imagine you are planning a fundraising event for your local community center to support youth programs. You decide to sell tickets at a cost of $8 each. You also decide that for every ticket sold, you need to allocate $9 for refreshments, decoration, and other expenses. If you want to raise a total of $144 from ticket sales after covering those costs, how many tickets do you need to sell?

Setting Up the Equation

To find how many tickets (x) you need to sell, you can set up the equation as follows:

1. Each ticket sells for $8, and there are extra costs of $9 per ticket.
2. The total amount you want to raise (after expenses) is $144.

This can be modeled with the equation:

\[ 8(x + 9) = 144 \]

Solving the Equation

We will solve the equation in two different ways.

Method 1: Distributing and Solving

1. Distribute 8 across the terms in the parentheses:

   \[ 8x + 72 = 144 \]

2. Subtract 72 from both sides:

   \[ 8x = 144 - 72 \] \[ 8x = 72 \]

3. Divide by 8:

   \[ x = \frac{72}{8} \] \[ x = 9 \]

This means you need to sell 9 tickets.

Method 2: Isolating x First

1. Start with the original equation:

   \[ 8(x + 9) = 144 \]

2. Divide both sides by 8:

   \[ x + 9 = \frac{144}{8} \] \[ x + 9 = 18 \]

3. Subtract 9 from both sides:

   \[ x = 18 - 9 \] \[ x = 9 \]

Again, we find that you need to sell 9 tickets.

Conclusion

Both methods yield the same result, \( x = 9 \).

Preferred Method

I personally preferred Method 2: Isolating x First because it is often quicker to manipulate the equation in a straightforward way by simplifying on both sides. It allows for a clearer understanding of the relationship between the variables and directly leads to the solution without having to deal with the additional distribution step initially. Additionally, this method often minimizes potential errors in calculations by reducing the number of operations performed in each step.

Short real life situations written like a 6 grader

Sure! Here are a couple of short real-life situations explained in a way a 6th grader could relate to:

Situation 1: The Bake Sale

You and your friends are having a bake sale to raise money for a school field trip. Each cupcake you sell costs $8, but you also need to buy supplies, which will cost $9 for each cupcake. If you want to make a total of $144 to save for the trip, how many cupcakes do you need to sell?

Situation 2: The Video Game Fundraiser

You really want to buy a new video game that costs $144. You decide to do some chores, and your parents agree to pay you $8 for each chore you complete. However, you need to spend $9 on some materials for your chores. If you want to have enough money for the video game, how many chores do you need to do?

Conclusion

In both situations, you can use the equation \( 8(x + 9) = 144 \) to find out how many items (cupcakes or chores) you need to complete to raise the money you want!

You and your friends are having a bake sale to raise money for a school field trip. Each cupcake you sell costs $8, but you also need to buy supplies, which will cost $9 for each cupcake. If you want to make a total of $144 to save for the trip, how many cupcakes do you need to sell? Solve 8(x+9)=144

Let's solve the equation \(8(x + 9) = 144\) step by step to find out how many cupcakes you need to sell for your bake sale.

Setting Up the Equation

1. Understand the Variables:
   • \(x\) = the number of cupcakes sold.
   • Each cupcake costs $8.
   • You also spend $9 on supplies for each cupcake.
   • You want to make a total of $144 after expenses.

Solve the Equation

Step 1: Distribute

First, distribute \(8\) across the terms in the parentheses:

\[ 8(x + 9) = 144 \]

Distributing gives:

\[ 8x + 72 = 144 \]

Step 2: Subtract 72

Next, subtract \(72\) from both sides of the equation:

\[ 8x + 72 - 72 = 144 - 72 \]

This simplifies to:

\[ 8x = 72 \]

Step 3: Divide by 8

Now, divide both sides by \(8\) to isolate \(x\):

\[ x = \frac{72}{8} \]

Calculating that gives:

\[ x = 9 \]

Conclusion

You need to sell 9 cupcakes to raise a total of $144 for your school field trip.