Final answer:
Two whole numbers A and B add up to 12, with a ratio of A:B of 1:3. By setting up equations based on these conditions, we find that A is 3 and B is 9, which satisfies both the sum and the ratio given in the problem.
Step-by-step explanation:
The question requires resolving a linear system involving two whole numbers, A and B, where their sum is 12 and the ratio of A to B is 1:3.
To find A and B, we can set up the following equations based on the given information:
A + B = 12 (the sum of A and B)
A/B = 1/3 (the ratio of A to B)
By multiplying the second equation by B, we get A = B/3.
Substituting A in the first equation, we get B/3 + B = 12.
Solving for B, we combine like terms to get (1/3)B + B = 12, which simplifies to (4/3)B = 12.
Multiplying both sides by 3/4 gives us B = 9.
Plugging B into the first equation, A + 9 = 12, we find A = 3.
Therefore, the whole numbers A and B are 3 and 9, respectively, which satisfies both the sum condition and the ratio condition.