Question 54277
I am going to show you step by step solutions for 2 and give you hints on the other 4.  If you have more questions, let me know.
1.
If the amount of $2.80 coffee =x
And the amount of $1.60 coffe =2 lbs
Then the amoung you have when you mix them together is: x+2
The price of $2.80 = 280 cents (it's easier to solve without decimals)
The price of $1.60 = 160
The price of the mixture $2.56=256 
Cost = Price*amount, so our equation is:
280x+160(2)=256(x+2)
280x+320=256x+512
-256x+280x+320=-256x+256x+512
24x+320=512
24x+320-320=512-320
24x=192
24x/24=192/24
x=8 
The amount of $2.80 coffe that should be added is {{{highlight(8 lbs)}}}
Check by substituting 8 in for x
$2.80(8)+$1.60(2)=$2.56(8+2)
$22.40+$3.20=$2.56(10)
$25.60=$25.60  Seems reasonable.
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2.
The trains are 450 miles apart and heading toward each other, so if we add their distances together we will get a total of 450 miles.
The formula you need to learn is: {{{highlight(d=rt)}}} where d= distance, r=rate or speed, and t=time.
They both travel a time of 6 hrs, so
Let time for the commuter train=6
Let time for the express train=6
Let RATE for the commuter train=x  (because we don't know anything about it)
Then RATE for the express train=x+25  (because it's 25 mph faster than the commuter train)
Then the distance for the commuter train is: 6x
The distance for the express is: 6(x+25)
The total distance:450 
PROBLEM to solve:
6x+6(x+25)=450
6x+6x+150=450
(6+6)x+150=450
12x+150=450
12x+150-150=450-150
12x=300
12x/12=300/12
x=25
The rate of the commuter train: {{{highlight(x=25 mph)}}}
The rate of the express train: x+25={{{highlight(25+25=50 mph)}}}
Check:
6(25)+6(50)=450
150+300=450
450=450 Seems reasonalbe.
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3.  Add the two distances together to get 198 (because they're travelling in opposite directions to add up to 198 miles apart.)
  Let the time for both =t (because they're both traveling the same amount of time)
Formula to use {{{highlight(d=rt)}}} 
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4.  Let the amount of students =x
Then all of the rest of the tickets= 1200-x
Then your problem is:
4x+15(1200-x)=12,786
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5. Let the time that the train traveled = t
Then the time that the bus traveled=t-1 (one hour less)
Set the two distances = to each other because they are traveling to the same town in a straight line.
Fromula to use {{{highlight(d=rt)}}} 
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6. Let the amount of rhododendrons=x
Then the amount of azaleas would = the rest of the 100 plants: 100-x
Set the problem up like #4.
Happy Calculating!!!