Question 53783: P+R=4
Q*P+R=10
P+Q*R=14
Find value of Q
I am not a student anywhere. My brother gave me this quiz and I can't solve it.
Answer by jenrobrody(19)   (Show Source):
You can put this solution on YOUR website! P+R=4
PQ+R=10
P+QR=14
To solve, add the second and third equations together:
PQ+R=10
+ P+QR=14
equals: PQ+R+P+QR=24
factoring: (R+P)+Q(P+R)=24
substituting 4 for P+R:
(4) + Q(4)=24
subtracting 4 from both sides:
4+4Q-4=24-4
4Q=20, dividing by 4:
Q=5.
Using R=4-P and PQ+R=10, we get:
5P+4-P=10
4P+4=10 subtracting 4,
4P=6 dividing by 4,
P=6/4 or 3/2=1.5
Using P=4-R and P+QR=14:
4-R+5R=14
4+4R=14 subtracting 4,
4R=10 dividing by 4,
R=10/4 or 5/2=2.5
so, Q=5, P=1.5, R=2.5
1.5+2.5=4 ok
5*1.5+2.5=7.5+2.5=10 ok
1.5+5*2.5=1.5+12.5=14 ok
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