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

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) (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) (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

RELATED QUESTIONS
Ken had some big and small packets of flour. The amount of flour in a big packet was 4... (answered by Boreal,greenestamps)
Hi ray sam tim had a total of $1017 at first. Rayhad the least amount of money. The... (answered by ankor@dixie-net.com)
. A bag contains 72 red marbles, 45 green marbles and 108 blue marbles. These are packed... (answered by Fombitz)
Pens are sold in packets of 15 pens per packet. The pens are of different colour and 20%... (answered by ewatrrr)
Blue stickers were sold in packet of 15 each. Green stickers were sold in packets of 40... (answered by Theo,MathTherapy)
Hi Mrs Taylor withdrew an equal number of $2 and $10 notes. She placed 40% of the 2... (answered by Theo)
Sam and tim have a total of 130 sweets; tim and claire have a total of 141 sweets; sam... (answered by stanbon)
For every 2 salt and vinegar crisps, there are 4 packets of plain crisps, 3 packets of... (answered by josmiceli)
Terry and Xavier had savings in the ratio of 3:2. They bought a gift for their friend and (answered by ikleyn,greenestamps)