9514 1404 393
Answer:
p : q = 3 : 2
Step-by-step explanation:
You are given sufficient information to write two relations involving p and q. We presume these will be sufficient to find an answer to the question. We will be able to find p and q. Then we can find their ratio, as the problem asks.
(p-15)/(q-15) = 2/1
(p+30)/(q+30) = 5/4
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From the first equation, we get ...
p -15 = 2(q -15)
p = 2q -15 . . . . . . . add 15, simplify
From the second equation, we get ...
4(p +30) = 5(q +30)
4p + 120 = 5q + 150
4p = 5q + 30
Using the first equation to substitute for p, we have ...
4(2q -15) = 5q +30
8q -60 = 5q +30 . . . eliminate parentheses
3q = 90 . . . . . . . . . . . add 60-5q to both sides
q = 30 . . . . . . . . . . . . divide by 3
p = 2q -15 = 2(30) -15 = 45
Then the desired ratio is ...
p : q = 45 : 30
p : q = 3 : 2
