Final answer:
To determine the value of b given a/b = 5 and 4a + 7b = 9, substitute a = 5b into the second equation and solve, resulting in b being 1/3.
Step-by-step explanation:
The question asks us to find the value of b given the conditions that a/b = 5 and 4a + 7b = 9. First, we rewrite the equation a = 5b (from a/b = 5). Then, we substitute 5b for a in the second equation:
To find the value of b, we can start by solving the equation a/b = 5 for a. This gives us a = 5b. Substituting this value of a into the second equation, 4a + 7b = 9, we get 4(5b) + 7b = 9. Simplifying this equation, we have 20b + 7b = 9. Combining like terms, we get 27b = 9. Dividing both sides by 27, we find that b = 1/3.
Substitute a = 5b into 4a + 7b = 9:
4(5b) + 7b = 920b + 7b = 9Combine like terms: 27b = 9Divide both sides by 27 to solve for b:b = 9/27b = 1/3
Therefore, the value of b is 1/3.