Certainly! Let's help Amanda figure out the mystery number with a step-by-step solution.
1. Identify the given clue and what it means:
- "A third of double this number minus four equals ten."
2. Set up the equation based on the clue:
- Let the mystery number be denoted by [tex]\( x \)[/tex].
- According to the clue, we can write the equation as:
[tex]\[
\frac{1}{3} \times (2 \times x) - 4 = 10
\][/tex]
3. Simplify the equation:
- First, simplify the expression inside the parentheses:
[tex]\[
\frac{1}{3} \times 2x - 4 = 10
\][/tex]
- This simplifies further to:
[tex]\[
\frac{2x}{3} - 4 = 10
\][/tex]
4. Isolate the fraction term:
- Add 4 to both sides of the equation to isolate the fraction term:
[tex]\[
\frac{2x}{3} = 14
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
- To remove the fraction, multiply both sides of the equation by 3:
[tex]\[
2x = 14 \times 3
\][/tex]
- Simplify the right side of the equation:
[tex]\[
2x = 42
\][/tex]
- Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{42}{2} = 21
\][/tex]
Therefore, the mystery number is [tex]\( 21 \)[/tex]. Amanda can use this solution to win the Math Challenge competition!
