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Chapter 6: Problem 76

Solve. $$ 15 \cdot y=75 $$

Short Answer

Expert verified
y = 5

Step by step solution

01

Identify the Equation

The given equation is: \(15y = 75\).
02

Isolate the Variable

To solve for \(y\), isolate the variable by dividing both sides of the equation by 15. This gives: \[ y = \frac{75}{15} \]
03

Simplify the Expression

Simplify the right-hand side: \( y = 5 \)

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Key Concepts

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

Isolating the Variable
Isolating the variable means getting the variable by itself on one side of the equation. In this problem, our goal is to solve for \( y \) in the equation \( 15y = 75 \). The first step is to isolate \( y \) by removing the coefficient (the number 15 that is multiplied by \( y \)). We do this by performing the opposite operation, which is division in this case. Divide both sides of the equation by 15:

Simplifying Expressions
After isolating the variable, the next step is often to simplify the expression. Simplification means making the equation as straightforward as possible, which sometimes involves performing arithmetic operations or reducing fractions. In our problem, after dividing both sides by 15, we get:
\[ y = \frac{75}{15} \]
Now, simplify the fraction by dividing the numerator (75) by the denominator (15):

\[ y = 5 \]

Simplifying expressions may also involve other operations, such as combining like terms or applying distributive properties, but in this case, it鈥檚 straightforward division.
Basic Algebra
Basic algebra is the foundation of solving equations like this. It involves understanding how to manipulate numbers and variables to find unknowns. Algebra helps us make sense of relationships between quantities and how they change.

Here鈥檚 a quick recap of what we did to solve the equation:

  • We identified the equation: \( 15y = 75 \)
  • We isolated the variable: \( y = \frac{75}{15} \)
  • We simplified the expression: \( y = 5 \)


Solving linear equations like this is one of the first steps in algebra. Mastering these simple manipulations will help you tackle more complex problems later on.

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