Final answer:
A and B are two numbers that sum to 44 and have a ratio of 4:7. By using substitution and solving the equations, we find that A is 16 and B is 28.
Step-by-step explanation:
The given equations are:
- A + B = 44
- A:B :: 4:7, which means A/B = 4/7
To find A and B, perform the following steps:
- Express A in terms of B using the ratio: A = (4/7)B.
- Substitute A in the first equation: (4/7)B + B = 44.
- Solve for B: (4/7)B + (7/7)B = 44, (11/7)B = 44, B = 44 × (7/11) = 28.
- Substitute B back into the ratio to find A: A = (4/7) × 28 = 16.
A is 16 and B is 28, satisfying both conditions.