SOLUTION: Need help solving these four questions: 1. How many pounds of coffee beans selling for $2.80 per pound should be mixed with 2 pounds of coffee beans selling for $1.60 a pound t

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Question 54277: Need help solving these four questions:
1. How many pounds of coffee beans selling for $2.80 per pound should be mixed with 2 pounds of coffee beans selling for $1.60 a pound to obtain mixture selling for $2.56 per pound?
2. Two trains, an express and a commuter, are 450 miles apart. Both start at the same time and travel toward each other. The meet 6 hours later. The speed of the express is 25 mph faster that the commuter. Find the speed of each train.
3. Two cars are traveling in opposite directions at average rates of 60 mph and 72 mph. How many hours will it take before the ars are 198 miles apart?
4. One thousand two hundred people attended a college basketball game. Student tickets cost $4 and all other tickets cost $15. If the receipts for the game totaled $12,786, how many of each kind of ticket was sold?
5. A train traveling at 40 miles per hour leaves for a certain town. One hour later, a bus traveling at 50miles per hour leaves for the same town and arrives at the same time as the train. If both the train and the bus traveled in a straight line, how far is the town from where they started?
6. A landscaper has a budget of $2250 to palnt 100 azaeleas and rhododendrons around a new office building. If there is a cost of $40 per rhododendron and $15 per azalea, how many of each can she plant?
When you give the answers please identify the variable, write the equation and show me how to solve the equation.
Answer by funmath(2933) (Show Source):
You can put this solution on YOUR website!
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
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.
:
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: 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:
The rate of the express train: x+25=
Check:
6(25)+6(50)=450
150+300=450
450=450 Seems reasonalbe.
:
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
:
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
:
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
:
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!!!