Question | Answer |
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 |
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 |
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) |
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 |
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) |
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 |
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 |
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 |
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 |
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 |