11 (35) Two whole numbers A and B satisfy the following conditions. Find A and B.

Question

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: $$A=33,B=15$$

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: $$\text{A = 33, B = 15}$$