Solving the Mystery of the Fruit Smoothie and Protein Bar Prices

Oct 13, 2025 by leolavanderia.com.br 73 views

Solving the Mystery of the Fruit Smoothie and Protein Bar Prices

In this article, we will delve into the world of mathematics and solve a real-life problem involving the prices of fruit smoothies and protein bars. We will use algebraic equations to find the cost of each item, making it a fun and interactive math problem.

Jake buys a fruit smoothie and a protein bar for $5.90. Kobe buys 2 fruit smoothies and 4 protein bars, paying $16.80. What is the cost of each fruit smoothie and each protein bar?

Let's denote the cost of a fruit smoothie as x and the cost of a protein bar as y. We can write two equations based on the given information:

x + y = 5.90 (Equation 1)
2x + 4y = 16.80 (Equation 2)

To solve these equations, we can use the method of substitution or elimination. In this case, we will use the elimination method.

First, let's multiply Equation 1 by 2 to make the coefficients of x in both equations equal:

2(x + y) = 2(5.90) 2x + 2y = 11.80

Now, we can subtract this new equation from Equation 2 to eliminate the variable x:

(2x + 4y) - (2x + 2y) = 16.80 - 11.80 2y = 5.00

Now that we have the value of 2y, we can divide both sides by 2 to find the cost of a protein bar (y):

y = 5.00 / 2 y = 2.50

Now that we have the value of y, we can substitute it into Equation 1 to find the cost of a fruit smoothie (x):

x + 2.50 = 5.90 x = 5.90 - 2.50 x = 3.40

In this article, we used algebraic equations to solve a real-life problem involving the prices of fruit smoothies and protein bars. We found that the cost of a fruit smoothie is $3.40 and the cost of a protein bar is $2.50.

This problem can be applied to real-life situations where we need to find the cost of multiple items. For example, if a store sells a combination of items, we can use algebraic equations to find the cost of each item.

When solving equations, always check your work by plugging the values back into the original equation.
Use the elimination method to eliminate variables and make the equations easier to solve.
Practice, practice, practice! The more you practice solving equations, the more comfortable you will become with the process.

In conclusion, solving equations is a fun and interactive way to apply mathematical concepts to real-life problems. By using algebraic equations, we can find the cost of multiple items and make informed decisions. Whether you are a student or a professional, understanding how to solve equations is an essential skill that will benefit you in many areas of life.
Frequently Asked Questions (FAQs) About Solving Equations

In our previous article, we solved a real-life problem involving the prices of fruit smoothies and protein bars using algebraic equations. In this article, we will answer some frequently asked questions (FAQs) about solving equations.

A: An equation is a statement that says two things are equal. It is a mathematical statement that contains an equal sign (=) and is used to solve for a variable.

A: A variable is a letter or symbol that represents a value that can change. In the equation x + y = 5.90, x and y are variables.

A: An expression is a group of numbers, variables, and mathematical operations that are combined to form a value. An equation is a statement that says two expressions are equal.

A: To solve an equation, you need to isolate the variable on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

A: The order of operations is a set of rules that tells you which operations to perform first when solving an equation. The order of operations is:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

A: The elimination method is a technique used to solve equations by eliminating one of the variables. To use the elimination method, you need to multiply both sides of one or both equations by a value that will make the coefficients of one of the variables the same.

A: The substitution method is a technique used to solve equations by substituting one of the variables into the other equation. The elimination method is a technique used to solve equations by eliminating one of the variables.

A: To check your work, you need to plug the values back into the original equation and make sure that the equation is true.

A: Some common mistakes to avoid when solving equations include:

Not following the order of operations
Not isolating the variable on one side of the equation
Not checking your work
Not using the correct method to solve the equation

In this article, we answered some frequently asked questions (FAQs) about solving equations. We hope that this article has helped you to better understand how to solve equations and has provided you with the confidence to tackle more complex equations in the future.

Practice, practice, practice! The more you practice solving equations, the more comfortable you will become with the process.
Use the elimination method to eliminate variables and make the equations easier to solve.
Check your work by plugging the values back into the original equation.
Avoid common mistakes such as not following the order of operations and not isolating the variable on one side of the equation.