Calculating the Calories in the Carrots and Hummus

Oct 13, 2025 by thesweetdesigns.com 97 views

A Bag of Baby Carrots and a Container of Hummus Dip: A Mathematical Snack Problem

In this article, we will delve into a mathematical problem involving a bag of baby carrots and a container of hummus dip. The problem states that a bag of baby carrots and a container of hummus dip contain a total of 650 calories. Rosarita, the protagonist, ate $\frac{3}{4}$ of the bag of carrots and $\frac{2}{7}$ of the container of hummus as a snack. Her snack contained a total of 260 calories. We will use mathematical concepts to solve this problem and understand the relationship between the calories consumed and the fractions of the snack eaten.

To begin, let's break down the problem and understand what is given and what is required. We are given that a bag of baby carrots and a container of hummus dip contain a total of 650 calories. This is the total amount of calories in both the carrots and the hummus. We are also given that Rosarita ate $\frac{3}{4}$ of the bag of carrots and $\frac{2}{7}$ of the container of hummus. This means that she ate a fraction of the total calories in both the carrots and the hummus.

Calculating the Calories in the Carrots and Hummus

Let's assume that the bag of carrots contains $x$ calories and the container of hummus contains $y$ calories. Since the total calories in both the carrots and the hummus is 650, we can write the equation:

x + y = 650

We are also given that Rosarita ate $\frac{3}{4}$ of the bag of carrots and $\frac{2}{7}$ of the container of hummus. This means that she ate $\frac{3}{4}x$ calories from the carrots and $\frac{2}{7}y$ calories from the hummus. The total calories she ate is 260, so we can write the equation:

\frac{3}{4}x + \frac{2}{7}y = 260

Solving the Equations

We have two equations and two variables. We can solve these equations using substitution or elimination. Let's use substitution. We can solve the first equation for $y$ :

y = 650 - x

Substituting this expression for $y$ into the second equation, we get:

\frac{3}{4}x + \frac{2}{7}(650 - x) = 260

Simplifying this equation, we get:

\frac{3}{4}x + \frac{1300}{7} - \frac{2}{7}x = 260

Combine like terms:

\frac{3}{4}x - \frac{2}{7}x = 260 - \frac{1300}{7}

Simplify the right-hand side:

\frac{21}{28}x - \frac{8}{28}x = \frac{1820 - 1300}{7}

Combine like terms:

\frac{13}{28}x = \frac{520}{7}

Multiply both sides by $\frac{28}{13}$ :

x = \frac{520}{7} \times \frac{28}{13}

Simplify:

x = \frac{14560}{91}

Now that we have found $x$ , we can find $y$ by substituting $x$ into one of the original equations. Let's use the first equation:

y = 650 - x

Substituting $x = \frac{14560}{91}$ , we get:

y = 650 - \frac{14560}{91}

Simplify:

y = \frac{59150 - 14560}{91}

Simplify:

y = \frac{44690}{91}

In this article, we solved a mathematical problem involving a bag of baby carrots and a container of hummus dip. We used mathematical concepts to find the total calories in both the carrots and the hummus, and then used substitution to solve for the calories in each. We found that the bag of carrots contains $\frac{14560}{91}$ calories and the container of hummus contains $\frac{44690}{91}$ calories. This problem demonstrates the importance of mathematical problem-solving in real-world scenarios.

The final answer is: $\boxed{260}$
A Bag of Baby Carrots and a Container of Hummus Dip: A Mathematical Snack Problem - Q&A

In our previous article, we solved a mathematical problem involving a bag of baby carrots and a container of hummus dip. The problem stated that a bag of baby carrots and a container of hummus dip contain a total of 650 calories. Rosarita, the protagonist, ate $\frac{3}{4}$ of the bag of carrots and $\frac{2}{7}$ of the container of hummus as a snack. Her snack contained a total of 260 calories. We used mathematical concepts to solve this problem and understand the relationship between the calories consumed and the fractions of the snack eaten.

Q: What is the total number of calories in the bag of baby carrots and the container of hummus dip? A: The total number of calories in the bag of baby carrots and the container of hummus dip is 650.

Q: What fraction of the bag of carrots did Rosarita eat? A: Rosarita ate $\frac{3}{4}$ of the bag of carrots.

Q: What fraction of the container of hummus did Rosarita eat? A: Rosarita ate $\frac{2}{7}$ of the container of hummus.

Q: How many calories did Rosarita eat in total? A: Rosarita ate a total of 260 calories.

Q: How many calories are in the bag of baby carrots? A: The bag of baby carrots contains $\frac{14560}{91}$ calories.

Q: How many calories are in the container of hummus dip? A: The container of hummus dip contains $\frac{44690}{91}$ calories.

Q: What mathematical concept was used to solve this problem? A: The mathematical concept of substitution was used to solve this problem.

Q: Why is it important to understand mathematical concepts like substitution? A: Understanding mathematical concepts like substitution is important because it allows us to solve real-world problems and make informed decisions.

Q: Can you explain the problem in simpler terms? A: The problem is about a bag of baby carrots and a container of hummus dip that together contain 650 calories. Rosarita ate a certain fraction of each, and we need to find out how many calories she ate in total.

Q: What is the significance of this problem? A: This problem demonstrates the importance of mathematical problem-solving in real-world scenarios. It shows how mathematical concepts can be applied to solve problems that involve fractions and proportions.

In this article, we answered some of the most frequently asked questions about the mathematical problem involving a bag of baby carrots and a container of hummus dip. We provided detailed explanations and examples to help readers understand the problem and its solution. We hope that this article has been helpful in clarifying any doubts and providing a deeper understanding of the mathematical concepts involved.

The final answer is: $\boxed{260}$