Discovering the Sale Price of Video Games
What equation could Maggie and Olivia use to find each video game's sale price, x?
Solution:
Let's set up equations for Maggie and Olivia's purchases:
- Maggie's purchase:
- She buys 6 video games at a sale price of x dollars each.
- She uses a $3 coupon for one of the games.
So, Maggie's total cost can be expressed as: 6x - 3 dollars.
- Olivia's purchase:
- She buys 4 video games at the same sale price of x dollars each.
- She also buys a joystick for $22.
Olivia's total cost can be expressed as: 4x + 22.
- According to the problem, Maggie and Olivia spend the same amount on their purchases. Therefore, we can set up the equation:
6x - 3 = 4x + 22.
To solve for x, follow these steps:
- Subtract 4x from both sides: 6x - 4x - 3 = 22.
- Combine like terms: 2x - 3 = 22.
- Add 3 to both sides: 2x = 25.
- Divide by 2: x = 25/2 = $12.50.
Therefore, the sale price (x) of each video game is $12.50.
Understanding the Calculation
Maggie's Purchase: Maggie bought 6 video games, but used a $3 discount coupon on one of them. This means she actually paid for 6 games minus the $3 discount, resulting in the equation 6x - 3.
Olivia's Purchase: Olivia bought 4 video games and additionally purchased a $22 joystick. Her total cost can be represented as 4x + 22, where each game cost x dollars.
Equating Maggie and Olivia's Purchases: By setting Maggie and Olivia's total costs equal to each other, we can solve for the sale price of each video game. This results in the equation 6x - 3 = 4x + 22.
Solving for x: By simplifying the equation and isolating x, we find that x = $12.50, which represents the sale price of each video game.
Final Thoughts
Understanding how to calculate the sale price of items can be beneficial for making informed purchasing decisions. In this scenario, Maggie spent the same amount as Olivia even though they bought different quantities and used discounts. By setting up and solving equations, we were able to determine the sale price of each video game. This skill of setting up equations and variables can be applied to various real-life situations to assess costs and make budget-friendly choices.