SOLUTION: Hi james has some matchsticks and sachets.if one matchstick is put into each sachet, he hss 2 matchsticks left.if he puts 2 matchsticks into each sachet he will have 24 sachets le

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Question 1044518: Hi
james has some matchsticks and sachets.if one matchstick is put into each sachet, he hss 2 matchsticks left.if he puts 2 matchsticks into each sachet he will have 24 sachets left. How many matchsticks and sachets does he have.
thank you
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
m= number of matchsticks
s= number of sachets
"If one matchstick is put into each sachet, he has 2 matchsticks left" translates as
m-s=2 .
"If he puts 2 matchsticks into each sachet he will have 24 sachets left" translates as
s-m%2F2=24 ,
because James has m%2F2pairs of matchsticks,
and he would use m%2F2 sachets.
Because I am not a fan of denominators,
I would multiply both sides of the equal sign times 2 tp transform
s-m%2F2=24 into the equivalent equation 2s-m=48 .
Now I have the system of equations
system%282s-m=48%2Cm-s=2%29 .
There are many ways to solve for m and s .
One way:
Adding both equations, I get
2s-m%2Bm-s=48%2B2 ---> highlight%28s=50%29
Substituting that calue for s in m-s=2 ,
I can get m-50=2 ---> m=50%2B2 ---> highlight%28m=52%29 .