<PRE><B>Question 139474</B>
3.) Flying to Kampala wit ha tailwind a plane averaged 158 km/h. On the retun trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.
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Let x = speed of the plane in still air
Let y = speed of the wind
Write an equation for each trip:
x + y = 158
x - y = 112
------------adding eliminates y, find x
2x = 270
x = {{{270/2}}}
x = 135 km/hr is the speed of he plane in still air
Find y using the equation: x + y = 158
135 + y = 158
y = 158 - 135
y = 23 km/ hr is the speed of the wind
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4.) The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
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Let x = no. of Sr tickets
let y = no. of child&#39;s tickets
write an equation for each day:
3x + 1y = 38
3x + 2y = 52
------------- subtracting eliminates x, find y
0x - 1y = -14
y = $14 is the cost of a child&#39;s tickets
Find x using the 1st equation:
3x + 14 = 38
3x = 38 - 14
x = {{{24/3}}}
x = $8 cost of a Sr ticket
Check solution in 2nd equation: 3(8) + 2(14)  = 52
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6.)A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?
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Let x = speed of the boat
Let y = speed of the current
Write a distance equation for each trip dist = time * speed
10(x+y) = 210
70(x-y) = 210
Simplify both equations, divide the 1st one by 10 and the 2nd one by 70, results:
x + y = 21
x - y = 3
-------------adding eliminate y, find x
2x = 24
x = {{{24/2}}}
x = 12 mph speed of the boat
then
12 + y = 21
y = 21 - 12
y = 9 mph speed of he current.
I&#39;ll let you check solutions in one of the original equations.
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7) The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54
students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
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Let x = no. of students in each van
Let y = no. of students in each bus
Write an equation for each school
8x + 8y = 240
4x + 1y = 54
Multiply the 2nd equation by 2 and subtract from the 1st equation
8x + 8y = 240
8x + 2y = 108
-----------------subtracting eliminates x, find y
you should be able to take it from here now
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8) The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
1x + 6y = 372
4x + 12y = 780
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Multiply the 1st equation by 2, subtract the 2nd equation
2x + 12y = 744
4x + 12y = 780
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you carry on from here
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9) Brenda&#39;s school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?
3x + 9y = 75
8x + 5y = 67
Multiply 1st equation by 8, and 2nd equation by 3
24x + 72y = 600
24x + 15y = 201
-------------------subtracting eliminates x, find y
Carry on from here
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10) Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the
cost each of one small box of oranges and one large box of oranges.
3x + 14y = 203
11x +11y = 220
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11) A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current?
12(x+y) = 336
14(x-y) = 336
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12) DeShawn and Shayna are selling flower bulbs for a school fundraiser. Customers can buy bags of windflower bulbs and bags of daffodil bulbs. DeShawn sold 10 bags of windflower bulbs and 12 bags of daffodil bulbs for a total of $380. Shayna sold 6 bags of windflower bulbs and 8 bags of daffodil bulbs for a total of $244. What is the cost each of one bag of windflower bulbs and one bag of daffodil
bulbs?
10x + 12y = 380
 6x +  8y = 244

I am totally out of time. Hope this helps. This many problems at once will usually not be considered by most tutors. </PRE>