find p/q if (2q^2-pq):(q^2-pq) = 2:3.
Write it out as an equation with fractions, and cross multiply.
(2q^2-pq)/(q^2-pq) = 2/3.
6q^2 -3pq = 2q^2 -2pq
4q^2 = pq
4q = p
p/q = 4
To find p/q, we can start by setting up an equation using the given ratio:
(2q^2 - pq) / (q^2 - pq) = 2/3
To solve this equation, we can start by cross-multiplying:
(2q^2 - pq) * 3 = 2 * (q^2 - pq)
Next, distribute and simplify the equation:
6q^2 - 3pq = 2q^2 - 2pq
Combine like terms:
6q^2 - 2q^2 - 3pq + 2pq = 0
4q^2 - pq = 0
Factor out q:
q(4q - p) = 0
Now we have two possible cases to consider:
Case 1: q = 0
If q = 0, then the equation becomes 4(0) - p(0) = 0. This doesn't give us any information about p/q.
Case 2: 4q - p = 0
Setting the expression inside the parentheses equal to zero gives us:
4q - p = 0
Rearranging the equation:
4q = p
So, we have found that p = 4q.
Therefore, p/q = 4q / q = 4.
Hence, p/q = 4.