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kesi

· started a discussion

· 1 Months ago

plz provide solution (Question: 300371.0 )

solution

Question:

If xy + x + y = 250, xz + x + z = 300, yz + y + z = 216, find the value of x + y + z?

Options:
A)

50.25

B)

40.5

C)

45.25

D)

48.25

Solution:

Ans: (c)

  

cyril R

· commented

· 1 Months ago

xy + x + y = 250
x(y + 1) = 250 – y
x =
250
1
y
y
-
+ ... (i)
xz + x + z = 300
z(x + 1) = 300 – x
z =
300
( 1)
x
x
-
+ =
300 (250 )
( 1)
1 250
1
y
y
y
y
- -
+
æ - ö + ç ÷ è + ø
z =
300(1 ) (250 )
1 250
y y
y y
+ - -
+ + -
z =
50 301
251
+ y
... (ii)
yz + y + z = 216
y
50 301
251
é + y ù
êë úû + y +
50 301
251
+ y
= 216
(50 + 301y2) + 251y + 50 + 301y = 54216
301y2 + 602y – 54166 = 0
y = 12.45
x =
(250 12.45)
1 12.45
-
+ = 17.66
z =
300 17.66
1 17.66
-
+
= 15.13
x + y + z = 12.45 + 17.66 + 15.13 = 45.25
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