SOLUTION: Hi Tim Sam and Xavier received some red packets. The total number of red packets sam and Xavier had is 3 times what tim had. The ratio of red packets sam had to Xavier was 3:7. If

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hi Tim Sam and Xavier received some red packets. The total number of red packets sam and Xavier had is 3 times what tim had. The ratio of red packets sam had to Xavier was 3:7. If      Log On

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Question 1207572: Hi
Tim Sam and Xavier received some red packets. The total number of red packets sam and Xavier had is 3 times what tim had. The ratio of red packets sam had to Xavier was 3:7. If Tim and Xavier had 155 red packets together how many did Tim have.
Found 2 solutions by Theo, mananth:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
this is what i get.

let T = the amount that tim had, S = the amount that sam had, X = the amount that xavier had.

you are given that:

S + X = 3T
S / X = 3 / 7
T + X = 155

from S / X = 3 / 7, solve for S to get S = 3X / 7

S + X = 3T becomes 3X / 7 + X = 3T
multiply both sides of this equation by 7 to get:
3X + 7X = 21T
combine like terms to get:
10X = 21T
solve for X to get:
X = 2.1T

T + X = 155 becomes T + 2.1T = 155 which becomes 3.1T = 155.
solve for T to get T = 50
solve for X to get X = 105

from S = 3X / 7, solve for S to get S = (3 * 105) / 7 = 45.

you now have:
T = 50
X = 105
S = 45

confirm as correct because ......

S + X = 3T becomes 45 + 105 = 150 = 3 * 50.
S / X = 3 / 7 becomes 45 / 105 = 3 / 7 when you divide both numerator and divisor by 15.
T + X = 155 becomes 50 + 105 = 155.

everything checks out.

your solution is T = 50.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Tim Sam and Xavier received some red packets. The total number of red packets sam and Xavier had is 3 times what tim had. The ratio of red packets sam had to Xavier was 3:7. If Tim and Xavier had 155 red packets together how many did Tim have.
T be the number of red packets Tim had.
S be the number of red packets Sam had.
X be the number of red packets Xavier had.
As per given conditions
S+X = 3T......................................1
S/X =3/7.......................................2
S= 3X/7
T+X =155......................................3
T= 155-x
S+X = 3T
3x/7 +X = 3(155-X)
multiply by 7
3x+7x = 21(155-X)
10x = 21*155-21X
31X = 21*155
x = 21*155/31
X=5*21
X= 105
T= 155-x
T= 155-105= 50
S=3X/7
S= 3*105/7
S = 15*3=45
Tim had 50 red packets.
CHECK
S/X = 45/105 = 3/7