To determine how many stickers Ming Teck had initially, let's follow a step-by-step approach to solve the problem.
### Step 1: Define the Variable
Let [tex]\( x \)[/tex] be the initial number of stickers Ming Teck had.
### Step 2: Giving Stickers to His Sister
Ming Teck gave 12 stickers to his sister.
After giving these away, he had:
[tex]\[ x - 12 \][/tex]
stickers remaining.
### Step 3: Giving [tex]\(\frac{1}{5}\)[/tex] of the Remainder to His Brother
Next, he gave [tex]\(\frac{1}{5}\)[/tex] of the remaining stickers to his brother.
The amount of stickers given to his brother is:
[tex]\[ \frac{1}{5} \times (x - 12) \][/tex]
Thus, the number of stickers left after giving to his brother is:
[tex]\[ (x - 12) - \frac{1}{5} \times (x - 12) \][/tex]
[tex]\[ = \frac{5}{5} \times (x - 12) - \frac{1}{5} \times (x - 12) \][/tex]
[tex]\[ = \frac{4}{5} \times (x - 12) \][/tex]
### Step 4: Relating to the Final Amount
According to the problem, after giving stickers to his sister and his brother, he was left with [tex]\(\frac{2}{3}\)[/tex] of his initial stickers.
Therefore, we have the equation:
[tex]\[ \frac{4}{5} \times (x - 12) = \frac{2}{3} \times x \][/tex]
### Step 5: Solve the Equation
To solve this equation, we need to find [tex]\( x \)[/tex].
[tex]\[ \frac{4}{5} \times (x - 12) = \frac{2}{3} \times x \][/tex]
Multiply both sides by 15 (the least common multiple of 5 and 3) to clear the fractions:
[tex]\[ 15 \times \frac{4}{5} \times (x - 12) = 15 \times \frac{2}{3} \times x \][/tex]
[tex]\[ 3 \times 4 \times (x - 12) = 5 \times 2 \times x \][/tex]
[tex]\[ 12 \times (x - 12) = 10 \times x \][/tex]
Expand and simplify:
[tex]\[ 12x - 144 = 10x \][/tex]
Isolate [tex]\( x \)[/tex]:
[tex]\[ 12x - 10x = 144 \][/tex]
[tex]\[ 2x = 144 \][/tex]
[tex]\[ x = 72 \][/tex]
### Step 6: Verify the Solution
Let's verify that this solution is correct:
- Initial stickers: [tex]\( x = 72 \)[/tex]
- Stickers remaining after giving 12 to his sister: [tex]\( 72 - 12 = 60 \)[/tex]
- Stickers given to his brother: [tex]\(\frac{1}{5} \times 60 = 12 \)[/tex]
- Stickers remaining after giving to his brother: [tex]\( 60 - 12 = 48 \)[/tex]
- According to the problem, he should be left with [tex]\(\frac{2}{3}\)[/tex] of his initial stickers: [tex]\(\frac{2}{3} \times 72 = 48 \)[/tex]
Both our calculation and the problem statement agree. Therefore, Ming Teck initially had:
[tex]\[ \boxed{72} \][/tex] stickers.
