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Chapter 6: Problem 46

Solve. $$ 29.44=25.6 \times y $$

Short Answer

Expert verified
y = 1.15

Step by step solution

01

Write Down the Equation

Start by writing down the given equation: \[ 29.44 = 25.6 \times y \]
02

Isolate the Variable

To solve for the variable \( y \), isolate \( y \) by dividing both sides of the equation by 25.6: \[ y = \frac{29.44}{25.6} \]
03

Simplify the Equation

Simplify the right-hand side by performing the division: \[ y = 1.15 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

mathematics
Mathematics is the study of numbers, shapes, patterns, and relationships. It involves various disciplines including algebra, calculus, geometry, and more. In this exercise, we're focusing on algebra, which deals with solving equations to find the value of unknown variables. Algebra is one of the foundational stones of mathematics as it helps in real-world problem-solving.
isolate variable
Isolating the variable is a crucial step in solving linear equations. This means getting the unknown variable, in this case, 'y', by itself on one side of the equation.

In our exercise, the original equation given is:
\[ 29.44 = 25.6 \times y \]
  • To isolate 'y', we need to remove the coefficient multiplying it.
  • This is achieved by dividing both sides of the equation by 25.6.

This process ensures that we maintain the equality of the equation, and effectively isolate 'y'.
division in equations
Division in equations is used to cancel out coefficients and isolate variables.

Let's look at our example again:
\[ 29.44 = 25.6 \times y \]
  • By dividing both sides of the equation by 25.6, we perform the inverse operation of multiplication.
  • This division simplifies the equation to: \[ y = \frac{29.44}{25.6} \]

The division process is straightforward but must be done carefully to avoid errors in calculation.
simplification of equations
Simplification of equations makes them easier to solve and understand. In our exercise, after dividing 29.44 by 25.6, we get:
\[ y = \frac{29.44}{25.6} \]
  • Performing this division results in: \[ y = 1.15 \]

Simplifying the equation confirms the solution. By getting rid of complex fractions or coefficients, we tidy up the equation making it neat and easy to interpret. Simplification is the final touch to solve most algebraic problems.

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Most popular questions from this chapter

The effective yield is the yearly rate of simple interest that corresponds to a rate for which interest is compounded two or more times a year. For example, if \(P\) is invested at \(12 \%,\) compounded quarterly, we multiply \(P\) by \((1+0.12 / 4)^{4},\) or \(1.03^{4}\). Since \(1.03^{4} \approx 1.126\), the \(12 \%\) compounded quarterly corresponds to an effective yield of approximately \(12.6 \% .\) In Exercises 47 and \(48,\) find the effective yield for the indicated account. The account pays \(9 \%\) compounded monthly.

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