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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.​

Respuesta :

wegnerkolmp2741o

Answer:

3:2

Step-by-step 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

Answer:

Step-by-step explanation:

p - 15 : q - 15 = 2 : 1

We know that when we use ratios, we're using fractions, so when we cross multiply:

1(p - 15) = 2(q - 15)

p - 15 = 2q - 30

p + 15 = 2q

p = 2q - 15     ....(1)

30 + p : q + 30 = 5 : 4

We know that when we use ratios, we're using fractions, so when we cross multiply:

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

120 + 4p = 150 + 5q

4p = 30  + 5q     .....(2)

Substituting (1) in (2), we get:

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

= 8q - 60 = 30 + 5q

3q - 60 = 30

3q = 90

= 30

Putting q = 30 in (1), we get:

p = 2 * 30 - 15

= 60 - 15

= 45

But we need to find the ratio of p : q (which is p/q)

So, 45 : 30

= 3 : 2

Hope this helps!

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