Question

11 (35) Two whole numbers A and B satisfy the following conditions. Find A and B.
A - B= 18
A: B is equivalent to 11 : 5.

Answer 1

To find the whole numbers A and B that satisfy the given conditions, we can set up the equations based on the information provided.

1. From the first condition, we have:
\[
A - B = 18
\]

2. 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:
\[
\text{A = 33, B = 15}
\]