To find the whole numbers A and B that satisfy the given conditions, we can set up the equations based on the information provided.
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From the first condition, we have: \[ A - B = 18 \]
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From the second condition, the ratio \( A : B = 11 : 5 \) can be expressed as: \[ \frac{A}{B} = \frac{11}{5} \] This implies that: \[ A = \frac{11}{5}B \]
Now, we can substitute the expression for A from the second equation into the first equation:
\[ \frac{11}{5}B - B = 18 \]
To simplify, we find a common denominator:
\[ \frac{11B}{5} - \frac{5B}{5} = 18 \]
This simplifies to:
\[ \frac{6B}{5} = 18 \]
Now, we can solve for \( B \) by multiplying both sides by 5:
\[ 6B = 90 \]
Dividing by 6 gives:
\[ B = 15 \]
Now we can find A using the equation \( A = B + 18 \):
\[ A = 15 + 18 = 33 \]
Therefore, the whole numbers A and B are: \[ A = 33, \quad B = 15 \]
To confirm, we can check the ratio:
\[ \frac{A}{B} = \frac{33}{15} = \frac{11}{5} \]
This verifies that the ratio is correct.
Thus, the solution is: \[ \text{A = 33, B = 15} \]
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