Question

A varies BC when B =4, C=9, A=6. Find C if A=20 and B=15

Answer 1

To solve for \( C \) when \( A = 20 \) and \( B = 15 \) given that \( A \) varies directly with \( B \) and \( C \), we can use the information provided to find a proportionality constant.

From the information given, we know that:

\[
A = k \cdot B \cdot C
\]

where \( k \) is a constant.

Using the values provided: when \( A = 6 \), \( B = 4 \), and \( C = 9 \),

\[
6 = k \cdot 4 \cdot 9
\]

Calculate \( k \):

\[
6 = k \cdot 36
\]
\[
k = \frac{6}{36} = \frac{1}{6}
\]

Now, we can use this constant \( k \) to find \( C \) when \( A = 20 \) and \( B = 15 \).

Using the equation:

\[
20 = \frac{1}{6} \cdot 15 \cdot C
\]

Multiply both sides by 6:

\[
120 = 15 \cdot C
\]

Now, solve for \( C \):

\[
C = \frac{120}{15} = 8
\]

Therefore, when \( A = 20 \) and \( B = 15 \), the value of \( C \) is \( \boxed{8} \).