The sum of three numbers multiplied by 2 is 18. The first number plus the second

Question

The sum of three numbers multiplied by 2 is 18. The first number plus the second number decreased by the third number is -15. Three times the second number increased by the third number is -9. If x is the first number, y is the second number, and z is the third number, what are the three numbers? The sum of the three numbers Increased by 8 is 29. The sum of the first number and the third number decreased by three times the second number is -7. Five times the first number decreased by the second number is 18. If the first number is a, the second number is b, and the third number is c what are the three numbers?

Explanation / Answer

1.The 3 nos are x, y ,z given : 2 (x+ y+z) = 18 = . x+y+z=9 -----(1)

: : x+y - z= 15 ------(2) and 3y +z = 9 ----(3)

eqn 1 - eqn 2 = > 2z = -6 and z = -3 substituting in eq3 3y - 3 = 9 => 3y = 12 and y =4 substitute y ,z values in eqn 1 => x + 4 - 3 = 9 => x = 8 , y =4 and z= - 3

2 . let the 3 nos are x, y ,z and we get the eqns as : x + y+ z+ 8 =29 ---(1)

x - 3y +z = - 7 ----(2) 5x - y = 18 ---(3)

eqn 1 - eqn2 => 4y+8 = 36 => 4y= 28 and y = 7 substitute in eqn 3 : 5x - 7 = 18 => 5x = 25 and x=5

. put x= 5 , y = 7 in eqn 1 : x+ y+ z= 21 =. 5+7+z= 21 => z=9 , y =7 and x=5

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