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Chapter 5: Problem 42

Solve. $$ 0.078=0.3 \cdot t $$

Short Answer

Expert verified
t = 0.26

Step by step solution

01

Identify the given equation

The equation provided is \[ 0.078 = 0.3 \cdot t \]
02

Isolate the variable 't'

To solve for \( t \), divide both sides of the equation by 0.3 to get: \[ t = \frac{0.078}{0.3} \]
03

Perform the division

Calculate the right-hand side of the equation: \[ t = \frac{0.078}{0.3} = 0.26 \]
04

Verify the solution

Substitute \( t \) back into the original equation to ensure it holds true: \[ 0.3 \cdot 0.26 = 0.078 \] Since the equation is satisfied, the solution is correct.

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Key Concepts

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

basic algebra
In basic algebra, we deal with simple mathematical relationships between numbers and variables. A variable is a symbol that stands for an unknown number we want to find out. Equations like 0.078 = 0.3 can look intimidating, but they follow simple rules. These rules include adding, subtracting, multiplying, and dividing both sides of the equation to maintain balance while isolating the variable we want to solve for.
solving for a variable
Solving for a variable means figuring out what number the variable represents. In the equation 0.078 = 0.3 t, the variable we need to solve for is 't'. The first step is to get 't' by itself on one side of the equation. We do this by performing operations that will isolate 't'. In this case, we divide both sides by 0.3, resulting in t = 0.078 / 0.3. This isolates 't' and makes it easier to solve for its value.
division in algebra
When we solve linear equations like 0.078 = 0.3 t by division, we're using one of the fundamental concepts in algebra. Division helps us get rid of coefficients (the numbers multiplying the variables). Here's how you do it:
  • Identify the coefficient (the number in front of the variable).
  • Divide both sides of the equation by this coefficient to isolate the variable.
Applying this to our example: t = 0.078 / 0.3. When you calculate it, you get t = 0.26.
verifying solutions
Verifying solutions ensures your answer is correct. After isolating and solving for 't' in 0.078 = 0.3 t, we found that t = 0.26. To verify, substitute 0.26 for 't' back into the original equation: 0.3 * 0.26 = 0.078. Since both sides equal 0.078, our solution t = 0.26 is correct! Always verify your solutions to avoid mistakes.

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