Four times one third of a number plus 4 is equal to 8. Find the number.
Understand the Problem
The question is asking us to find a number based on the equation formed by the expression 'four times one third of a number plus 4 is equal to 8'. We will translate this into a mathematical equation, solve for the number, and find its value.
Answer
The value of the number is $3$.
Answer for screen readers
The value of the number is $3$.
Steps to Solve
- Translate the expression into an equation
We are given the expression 'four times one third of a number plus 4 is equal to 8'.
Let the number be represented by $x$. The expression can be translated into the following equation: $$ 4 \left( \frac{1}{3} x \right) + 4 = 8 $$
- Simplify the equation
Now, we'll simplify the left side of the equation.
Distributing $4$ gives: $$ \frac{4}{3} x + 4 = 8 $$
- Isolate the variable term
Next, we need to isolate the term with $x$.
Subtract $4$ from both sides: $$ \frac{4}{3} x = 8 - 4 $$
Which simplifies to: $$ \frac{4}{3} x = 4 $$
- Solve for the variable
Now, we want to solve for $x$ by multiplying both sides by the reciprocal of $\frac{4}{3}$, which is $\frac{3}{4}$: $$ x = 4 \cdot \frac{3}{4} $$
- Calculate the value of x
Now we can calculate the value: $$ x = 3 $$
The value of the number is $3$.
More Information
The problem showcases how to translate a verbal expression into a mathematical equation. It also demonstrates solving a linear equation by isolating the variable, which is a fundamental skill in algebra.
Tips
- Forgetting to distribute correctly when handling coefficients.
- Misplacing signs when moving terms across the equals sign, especially when subtracting or adding.
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