Question

For a given input value
\[q\], the function
\[g\] outputs a value
\[r\] to satisfy the following equation.
\[-7q+12r=3q-4r\]
Write a formula for
\[g(q)\] in terms of
\[q\].

Answer 1

Solve for r:

-7q + 12r = 3q - 4r
Add 4r to both sides: -7q + 16r = 3q
Add 7q to both sides: 16r = 10q
Divide by 16: r = (10/16)q = (5/8)q

Thus g(q) = (5/8)q.