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Question 104889: question 1) how many pounds of nuts selling at 6.00 lb. and raisins at 3.00 lb. should be combined to obtain 60 lbs of trail mix selling for 5.00 lb?
question 2) if a plane can travel 440 mph into the wind and 500 mph with the wind find the speed of the wind and the speed of the plane in still air?
question 3) at the beginning of a bike ride mary and sue are 30 miles apart. If they leave at the same time and ride in the same direction mary over takes sue in 6 hours. if they ride toward each other they pass each other in 1 hour. what are their speeds?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! It is best to ask one question per question, not a set of questions. One tutor might not want to tackle 3 questions at any given point in time. Also, by asking 3 questions, you could get 3 tutors working at once, which speeds getting your overall set of replies.
1) In this case, you know that there will be 60 lbs of trailmix. So there will be x lb or nuts and 60-x lb of raisins. You're told the 60 lb will sell for 5.00, so the total value will be 60*5 = 300.
Nuts sell for 6 and raisins sell for 3, so:
6(x) + 3(60-x) = 300.
6x + 180 -3x = 300.
Combining terms:
3x + 180 = 300
Subtracting 180 from both sides
3x = 120
Dividing by 3
x = 40
So, there will be 40 lb of nuts and 60-40=20 lb of raisins.
ALWAYS check.
6(40)+3(20)=300
240+60=300
300=300
Check!
2) The plane flying East (let's say) can travel 440 mph. Flying West, it can fly 500 mph. The wind would slow the plane in one direction, and speed it on its way the other way. So, we can write two equations:
x - s = 440 (where s= wind speed)
x + s = 500 (where s= wind speed)
Subtracting the second equation from the first, we have
-2s = -60
Dividing by -2:
s = 30.
So the wind speed = 30.
In turn that means the plane flies at 470 mph in still air.
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