Question

the value of a is directly proportional to the value of b. if a=21 when b=3, what is the value of a when b = 5? a) 18 b) 23 c) 24 d) 29 e) 35

Explanation:

Step1: Define direct proportionality

If \( a \) is directly proportional to \( b \), we can write the relationship as \( a = kb \), where \( k \) is the constant of proportionality.

Step2: Find the constant \( k \)

We know that when \( a = 21 \) and \( b = 3 \). Substitute these values into the equation \( a = kb \):
\( 21 = k \times 3 \)
To find \( k \), divide both sides by 3:
\( k=\frac{21}{3}=7 \)

Step3: Find \( a \) when \( b = 5 \)

Now that we know \( k = 7 \), we use the equation \( a = kb \) again. Substitute \( k = 7 \) and \( b = 5 \):
\( a = 7\times5 = 35 \)

Answer:

E) 35