To solve this problem, we first need to understand what it means for p to vary directly as q. When we say that p varies directly as q, we can express this relationship mathematically as:
p = kq
where k is the constant of proportionality.
From the information given, we know that when q = 31.2, p = 20.8. We can use these values to find the value of k.
Substituting the values into the equation:
20.8 = k * 31.2
To find k, we divide both sides by 31.2:
k = 20.8 / 31.2
Calculating this gives:
k = 0.6654 (approximately)
Now that we have k, we can find p when q = 15.3. We use the direct variation equation again:
p = k * q
Substituting the value of k and q:
p = 0.6654 * 15.3
Calculating this gives:
p ≈ 10.185 (approximately)
So, when q = 15.3, the value of p is approximately 10.185.