first and most helpful answer gets 10 points!
1) the math club and the science club had fundraisers to buy supplies for a hospice. the math club spent $135 buying six cases of juice and one case of bottled water. the science club spent $110 buying four cases of juice and two cases of bottled water. how much did a case of juice cost? how much did a case of bottled water cost?
2) kay spends 250 min/week exercising. her ratio of time spent on aerobics to time spent on weight training is 3 to 2. how many minutes per week does she spend on aerobics? how many minutes per week does she spend on weight training?
3) a light plane flew from its home base to an airport 255 miles away. with a head wind, the trip took 1.7 hours. the return trip with a tail wind took 1.5 hours. find the average airspeed of the plane and the average windspeed.
thanks if you help me :]
1) with x as juice and y as water
6x+y=135
4x+2y=110
therefore, y=135-6x
4x+2(135-6x)=110
4x+270-12x=110
-8x+270=110
-8x=-160
x=20
6(20)+y=135
120+y=135
y=15
So 15 dollars
2) a ratio is like this, if she spends 3 minutes on aerobics, she spends 2 minutes on weight. Therefore, 2/5 of her time is on weight training. So, 250*2/5=100 minutes/week.
3) so we have 255 miles to go to, so the overall trip takes 510 miles (back and forth). The total time is 1.7 hours + 1.5 hours, or 3.2 hours.
Therefore, 510/3.2 = average speed or 159.375 miles per hour.
the average speed with head wind is 255/1.7= 150 miles per hour.
the average speed with tail wind is 255/1.5 = 170 miles per hour.
Therefore, the average windspeed is 10 miles per hour because (170-150)/2=10
Hope this helps and can I please have 10 pts.
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