P and q are two numbers such that p > q. When you subtract 15 from p and subtract 15 from q answers are in 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

The value of p and q is 45 and 30 respectively equivalent to 3 : 2 in it's simplest form

Given:

p - 15 / q - 15 = 2/1

cross product

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

p - 15 = 2q - 30

p - 2q = -30 + 15

p - 2q = - 15 (1)

p + 30 / q + 30 = 5/4

cross product

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

4p + 120 = 5q + 150

4p - 5q = 150 - 120

4p - 5q = 30 (2)

p - 2q = - 15 (1)

4p - 5q = 30 (2)

multiply (1) by 4

4p - 8q = -60 (3)

4p - 5q = 30 (2)

subtract (2) from (3)

-8q - (-5q) = -60 - 30

-8q + 5q = -90

-3q = - 90

q = -90/-3

q = 30

substitute into p - 2q = - 15

p - 2(30) = -15

p - 60 = -15

p = -15 + 60

p = 45

Therefore, the ratio of p and q is 45 : 30

= 3 : 2

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The ratio of p:q is 3:2.

Step-by-step explanation:

It is given that,

When you subtract 15 from p and subtract 15 from q, the answers are in ratio 2 : 1.

The equation can be framed as,

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

p - 15 = 2(q - 15)  

p - 15 = 2q - 30

p = 2q - 15   equation (2)

When you add 30 to p and add 30 to q the answers are in the ratio 5 : 4.

(p + 30)/(q + 30) = 5/4   equation (3)

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

4p + 120 = 5q + 150

4p = 5q + 30   equation (4)

Substitute eq (2) p = 2q - 15 in eq (4),

⇒ 4 (2q - 15) = 5q + 30

⇒  8q - 60 = 5q + 30

⇒  3q = 90

⇒ q = 90/3

⇒ q = 30

Solving for p, substitute q=30 in eq (2),

⇒ p = 2q - 15

⇒  p = 2(30) - 15

⇒ p = 60-15

⇒ p = 45

To find the ratio of p : q,

we found that, p= 45 and q= 30

Therefore, p/q = 45/30 ⇒ 3/2

∴ The ratio of p:q is 3:2.

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.

income. 10x+1300

expenses 3x+(1800+1500)

expenses 3x+3300

to break even:

income = expense,

10x + 1300 = 3x + 3300,

solve for x.

step-by-step explanation:

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