Question

P and q are two numbers such that p > q

When you subtract 15 from p and subtract 15 from a the
answers are in the ratio 2 : 1
When you add 30 to p and add 30 to q the answers are in the
ratio 5:4
Find the ratio p:q
Give your answer in its simplest form.​

Answer 1

3:2

Explanation:

p-15: q-15

2:1

Using cross products

p-15 = 2(q-15)

p -15 =2q -30

Add 30 to each side

p +15 = 2q

p =2q - 15

30+p: q+30

5 :4

Using cross products

4(30+p) = 5(30+q)

120+4p = 150+5q

Subtract 120 from each side

4p = 30 +5q

Substitute the first equation in

4(2q -15) = 30 +5q

8q -60 = 30 +5q

Subtract 5q

3q -60 = 30

3q = 90

q = 30

Find p

p =2q - 15

p = 2*30 -15

p = 60-15

p = 45

ratio of p:q

45:30

Divide by 15

45/15 : 30/15

3:2