Beverly Has A Bag Of Marbles That Weighs 30 Grams. She Knows That Each Marble Weighs 1.5 Grams And The Bag Itself Weighs 1.5 Grams.Which Equation Could She Use To Determine How Many Marbles Are In The Bag? Select All That Apply.A. [$(1.5)x + 1.5 =

Mar 12, 2025 by ADMIN 248 views

Solving the Marble Mystery: A Mathematical Equation

In this article, we will delve into the world of mathematics and explore a real-life scenario that involves solving an equation to determine the number of marbles in a bag. Beverly has a bag of marbles that weighs 30 grams, and she knows that each marble weighs 1.5 grams and the bag itself weighs 1.5 grams. We will examine the equation that Beverly can use to determine how many marbles are in the bag.

To solve this problem, we need to understand the given information and what we are trying to find. We know that the total weight of the marbles and the bag is 30 grams. We also know that each marble weighs 1.5 grams and the bag itself weighs 1.5 grams. We want to find the number of marbles in the bag.

To determine the number of marbles in the bag, Beverly can use the following equation:

A. ${$ (1.5)x + 1.5 = 30}$

This equation represents the total weight of the marbles and the bag, which is 30 grams. The left-hand side of the equation represents the weight of the marbles, which is 1.5 grams per marble, multiplied by the number of marbles (x), plus the weight of the bag (1.5 grams).

Let's break down the equation and understand what each part represents:

$(1.5)x$ : This represents the weight of the marbles, which is 1.5 grams per marble, multiplied by the number of marbles (x).
+ 1.5: This represents the weight of the bag, which is 1.5 grams.
= 30: This represents the total weight of the marbles and the bag, which is 30 grams.

To solve the equation, we need to isolate the variable x, which represents the number of marbles. We can do this by subtracting 1.5 from both sides of the equation:

$(1.5)x + 1.5 - 1.5 = 30 - 1.5$

This simplifies to:

$(1.5)x = 28.5$

Next, we can divide both sides of the equation by 1.5 to solve for x:

$(1.5)x / 1.5 = 28.5 / 1.5$

This simplifies to:

$x = 19$

Therefore, there are 19 marbles in the bag.

In this article, we explored a real-life scenario that involved solving an equation to determine the number of marbles in a bag. We examined the equation that Beverly can use to solve the problem and broke down the equation to understand what each part represents. We then solved the equation to find the number of marbles in the bag, which is 19.

In addition to the equation A. ${$ (1.5)x + 1.5 = 30}$, there are other possible equations that Beverly can use to solve the problem. These equations include:

B. ${$ (1.5)x = 28.5}$
C. ${$ x = 19}$
D. ${$ (1.5)x + 1.5 - 1.5 = 30 - 1.5}$

These equations represent different ways of solving the problem, but they all lead to the same solution: there are 19 marbles in the bag.

In conclusion, solving the marble mystery involves using a mathematical equation to determine the number of marbles in a bag. By understanding the given information and breaking down the equation, we can solve for the variable x, which represents the number of marbles. This problem is a great example of how mathematics can be applied to real-life scenarios to solve problems and find solutions.
Frequently Asked Questions: Solving the Marble Mystery

In our previous article, we explored the problem of determining the number of marbles in a bag using a mathematical equation. We examined the equation that Beverly can use to solve the problem and broke down the equation to understand what each part represents. In this article, we will answer some frequently asked questions related to the problem.

A: The weight of each marble is 1.5 grams.

A: The weight of the bag is 1.5 grams.

A: The total weight of the marbles and the bag is 30 grams.

A: To solve the equation, you can follow these steps:

Subtract 1.5 from both sides of the equation to isolate the term with the variable x.
Divide both sides of the equation by 1.5 to solve for x.

A: The equation that you can use to solve the problem is:

$(1.5)x + 1.5 = 30$

A: There are 19 marbles in the bag.

A: Yes, you can use a different equation to solve the problem. For example, you can use the equation:

$(1.5)x = 28.5$

$x = 19$

A: If you make a mistake in solving the equation, you can try again or check your work to see where you went wrong. You can also use a calculator or a computer program to help you solve the equation.

A: Yes, you can apply this problem to real-life situations. For example, you can use this problem to determine the number of items in a package or the number of people in a group.

In this article, we answered some frequently asked questions related to the problem of determining the number of marbles in a bag using a mathematical equation. We provided step-by-step instructions on how to solve the equation and answered questions about the weight of each marble, the weight of the bag, and the total weight of the marbles and the bag. We also discussed how to apply this problem to real-life situations.

If you want to learn more about solving equations and applying mathematical concepts to real-life situations, you can check out the following resources:

Online math tutorials and videos
Math textbooks and workbooks
Math apps and software
Online communities and forums for math enthusiasts