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Question 1179223: 1)Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens. The girls plan to play as many games as they can before running out of tokens. Write an expression to represent the total number of tokens that Janie and Jasmine will need to play each of the three games at least once. Let m represent the number of games that require 2 n tokens; represent the number of games that require 3 p tokens, and represent the number of games that require 4 tokens.
2)Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens. The girls plan to play as many games as they can before running out of tokens. Let m represent the number of games that require 2 tokens; n represents the number of games that require 3 tokens, and p represents the number of games that require 4 tokens. Janie plays the 3-token game four times and Jasmine plays the 4-token games 5 times. Write two equivalent expressions to represent the number of tokens that the girls will need to play each of the three games at least one time.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down each part of the problem:
**1) Expression for Total Tokens (General Case):**
* **Games with 2 tokens:** m (number of games) * 2 (tokens per game) = 2m tokens
* **Games with 3 tokens:** n (number of games) * 3 (tokens per game) = 3n tokens
* **Games with 4 tokens:** p (number of games) * 4 (tokens per game) = 4p tokens
To play each of the three games at least once, they need to play at least one game of each type. Therefore, the total number of tokens needed is:
**Expression:** 2m + 3n + 4p
**2) Expressions for Total Tokens (Specific Case):**
* **Janie's Games:**
* She plays the 3-token game 4 times. So n=4.
* **Jasmine's Games:**
* She plays the 4-token game 5 times. So p=5.
* They will play each of the three games at least one time. So m=1.
Now, we can write the expression using the given values:
* 2m + 3n + 4p = 2(1) + 3(4) + 4(5) = 2 + 12 + 20 = 34 tokens.
To write two equivalent expressions, we can simply rearrange the terms:
* **Expression 1:** 2(1) + 3(4) + 4(5) = 34
* **Expression 2:** 4(5) + 3(4) + 2(1) = 34
**Answer:**
1. The expression for the total number of tokens is 2m + 3n + 4p.
2. Two equivalent expressions are 2(1) + 3(4) + 4(5) = 34 and 4(5) + 3(4) + 2(1) = 34.
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