SOLUTION: What is the value of Q for the following sets of equations: P + R = 4; Q x P + R = 10; P + Q x R = 14

Question 637356: What is the value of Q for the following sets of equations:
P + R = 4; Q x P + R = 10; P + Q x R = 14
Found 2 solutions by god2012, DrBeeee:
Answer by god2012(113) (Show Source): You can put this solution on YOUR website!
P + R = 4 --------------EQUATION 1
QP + R = 10-------------EQUATION 2
P + QR = 14-------------EQUATION 3
ADD EQUATION 2 AND 3
QP + R + P + QR = 24
P(1 + Q) + R(1 + Q) = 24
(1 + Q) (P + R) = 24
1 + Q = 24 / 4 = 6 (FROM EQUATION 1, P + R =4 )
Q = 6 -1 = 5
Q = 5

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Given
(1) P + R = 4
(2) QP + R = 10
(3) QR + P = 14
Recognize that you need the products QP and QR, so simply multiple both sides of (1) by Q and obtain
(4) QP + QR = 4Q
Now add (2) and (3) to obtain
(5) QP + QR + R + P = 10 + 14
Substitute (4) into (5) to get
(6) 4Q + R + P = 24
Substitute (1) into (6) to get
(7) 4Q + 4 = 24
4Q = 20
Q = 5
Now substitute Q into (2)
(2)' 5P + R = 10
Use (2)' and (1) to solve simultaneously to get P nad R
5P + R = 10
P + R = 4
5(4 - R) + R = 10
20 - 5R + R = 10
4R = 10
R = 5/2
Use (1) and R to get
P + 5/2 = 4
P = 3/2
Now check your answers in (2) and (3)
Is (5*(3/2) + 5/2 = 10)?
Is (15/2 + 5/2 = 10)?
Is (20/2 = 10)?
Is (10 = 10)? Yes
Is (5*(5/2) + 3/2 = 14)?
Is (25/2 + 3/2 = 14)?
Is (28/2 = 14)?
Is (14 = 14)? Yes
Your answer is P = 3/2, Q = 5 and R = 5/2
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