Question

Assume that a varies directly as b. When the value of a is 5, the value of bis 18.

When the value of a is 22, what is the value of b?
A) 70
B) 75
C) 79.2
D) 79

Answer 1

Using the direct variation equation and the given values, the constant of variation is calculated and then used to determine the value of b when a is 22, resulting in b being 79.2. (Option C).

Step-by-step explanation:

Since a varies directly as b, we can express their relationship with the equation a = kb, where k is the constant of variation.

Given that when a is 5, b is 18, we can find k by plugging in these values: 5 = k(18).

Solving for k, we get k = 5/18.

Now, we can use this constant to find the value of b when a is 22.

Plugging 22 into the equation gives us 22 = (5/18)b.

To solve for b, divide both sides by (5/18), resulting in b = (22 × 18) / 5, which simplifies to b = 79.2.

Therefore, the correct answer is Option C) 79.2.