Let the total number of toy cars in Bashir's collection be denoted as \( T \). We know the following from the problem:
- The total number of toy cars on the wall is 136.
- The number of toy cars in the display case is 15% of the total collection, which can be represented mathematically as \( 0.15T \).
Since all the toy cars either are in the display case or on the wall, we can express this relationship as:
\[ T = \text{(Number of cars in display case)} + \text{(Number of cars on the wall)} \]
Substituting in the known values:
\[ T = 0.15T + 136 \]
To isolate \( T \), we first subtract \( 0.15T \) from both sides:
\[ T - 0.15T = 136 \]
This simplifies to:
\[ 0.85T = 136 \]
Next, to solve for \( T \), we divide both sides by 0.85:
\[ T = \frac{136}{0.85} \]
Calculating the right-hand side:
\[ T = 160 \]
Thus, the total number of toy cars in Bashir's collection is \( \boxed{160} \).
To verify, we can check how many cars are in the display case:
\[ 0.15 \times 160 = 24 \]
Now, the total number of cars combines the display case and the wall:
\[ 24 + 136 = 160 \]
The calculations match, confirming that the total number of toy cars is correctly \( \boxed{160} \).
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