Module 7 - Solving Systems of Linear Equations and Problem Solving
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| The sum of two numbers is 76 and their difference is 52. Find the two numbers | X + Y = 76 64 + Y = 76
X - Y = 52 Y = 76 - 64
2X = 128 Y = 12
X=64
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| Three times one number minus a second is 8, and the sum of the numbers is 12. Find the numbers. | 3X - Y = 8 5 + Y = 12
X + Y =12 -5 -5
4X = 20 Y =7
X= 5
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| Last month, Jerry Papa purchased two DVDs and give CDs at wall-to-wall sound for $65. This month, he bought four DVDs and three CDs for $81. Find the price of each DVD and find the price of each CD. | 2X + 5Y = 65 -4X - 10Y = -130
4X + 3Y = 81 4X + 3Y = 81
-7Y = -49
Y= 7 X=15
(Plug Y into equation)
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| Sara and Keith Robinson purchased 40 stamps, a mixture of 44cent and 20 cent stamps. Find the number of each type of stamp if they spent $16.40 | .44X + .20Y = 16.40
X+Y= 40
(move decimal so you work with whole numbers)
44X+20Y = 1640
/4 /4 /4
11X+5Y = 410
X+Y= 40 (-.5)
35 + Y=40
-35 -35
Y=5
11X+5Y = 410
-5X-5Y = -200
6X=210
X=35
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| Pratap Puri rowed 18 miles town the Delaware River in 2 hours, but the return trip took 4 1/2 hours. Find the rate Pratap can row in still water and find the rate of the current. Let x = rate Pratap can row in still water and y = rate of current. | Create a chart.d&downriv=18, distance&upriv=18. downriv&r=x+y, downriv&t=2. Upriv&r=x-y, upriv&t=4.5
18=2(x+y)--> 9=x+1
18=4.5(x-y)(4)--> 36=9(x-y)
4x-y
x+y=9
x-y=4
2x=13 x=61/2 (plug that in and find that y= 2.5)
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| Elise is preparing 15 liters of a 25% saline solution. Elise has two other saline solutions, with strengths of 40&10%. Find the amount of 40% solution and the amount of 10% solution she should mix to get 15 liters of a 25% solution. | x+y=15 x+y=15(-1) -x-y=-15
4x+.1y=.25(.15) 4x+y=37.5 4x+y=37.5
3x=22.5, x=7.5
y=15-7.5, y=7.5
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| According to the MUTCD, a sign must have a perimeter of 60in. Also, its length must be 6 inches longer than its width. Find the dimensions. | p=2l+2w 60=2(w+6)+2w
p=60 60=2w+12+2w
l=12+6 60 = 4w+12
w=12 l=18 48=4w
w=12
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| Find the values of x and y in the isosceles triangle when (3x-10)degrees is an angel outside of the bottom left point. | x+y=180dg
x+2y=180dg
y+3x-10=180dg
x=180-2y
y+3(180-2y)-10=180
y+540-6y=190
-5y=190-540
-5y=350
y=70
x=180-70(2)=40
x=40
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| Judy plans to erect 152 feet of fencing around her rectangular horse pasture. A river bank serves as one side length on the rectangle. If each width is 4 ft longer than half the length, find the dimensions. | 2x+y+8+y=152
y+8+y=152
2y=152-8=144
2y=144
y=72
x=y/2+4
x=72/2+4
36+4=40
x=40
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| One number is two more than the second number. Twice the first is 4 less than 3 times the second. Find the numbers | X= Y +2
2X = 3Y - 4
2Y + 4 = 3Y - 4
2Y - 3Y = -4 . 4 - Y = -8
2X- 4 = 3 (-8)
2X - 4 = -24
+4 = -20
2X=-20
X=-10
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