Question

If x + 3 is directly proportional to y when x = 3 y = 8 what is x when y = 4

Answer 1

If \( x + 3 \) is directly proportional to \( y \), we can express this relationship mathematically as:

\[
x + 3 = k \cdot y
\]

for some constant \( k \).

We know that when \( x = 3 \), \( y = 8 \). Substituting these values into the equation allows us to solve for \( k \):

\[
3 + 3 = k \cdot 8
\]
\[
6 = k \cdot 8
\]
\[
k = \frac{6}{8} = \frac{3}{4}
\]

Now that we have the constant of proportionality \( k \), we can rewrite the proportional relationship:

\[
x + 3 = \frac{3}{4} y
\]

Next, we want to find \( x \) when \( y = 4 \). Substituting \( y = 4 \) into the equation gives:

\[
x + 3 = \frac{3}{4} \cdot 4
\]
\[
x + 3 = 3
\]

Now, solving for \( x \):

\[
x = 3 - 3
\]
\[
x = 0
\]

Thus, when \( y = 4 \), \( x \) is \( 0 \).