Solving systems of equations using Substitution method and elimination

zee-f · 2011-07-03 03:42:25

thanx )

bobbym · 2011-07-03 03:43:58

Well, what is your answer? I do not see it yet...

Bob · 2011-07-03 03:44:44

hi zee-f

Maybe you need to see the English translated into math.

Three times the width exceeds twice its length by two inches.

3 widths minus 2 lengths is 2

3W - 2L = 2

re-arrange

3W = 2L + 2

Four times its length is twelve more than its perimeter

So out of 4L and P, one needs to have 12 added, to get the other.

But which?

Well it says 4L is bigger so you must have to add 12 to P to get 4L

4L = P + 12

But also P = 2L + 2W

so

4L = (2L + 2W) + 12

take 2L off each side

2L = 2W + 12

Does that help?

Bob

Last edited by Bob (2011-07-03 03:54:20)

zee-f · 2011-07-03 07:37:01

thanx alot it sure did help

zee-f · 2011-07-03 07:45:28

i did number 4 i was wondering if it was correct

2x-5y=3
4x+3y=71

2x+3y=3 by 2 and minus 4x+3y=71

4x-10y=6
4x+3y=71
0x-13y=-65
y=-65/-13

y=5

2x=3+5(5)
2x=3+25
2x=28
x=14

numbers are 14 and 5

bobbym · 2011-07-03 07:46:47

Hi;

That is correct! Did they teach you how to check?

zee-f · 2011-07-03 07:46:58

6. A piece of wire 42 cm long is bent into a rectangle whose length is twice its width. Find the dimensions of the rectangle.
AThe rectangle is 12 cm long and 9 cm wide
BThe rectangle is 10 cm long and 11 cm wide.
CThe rectangle is 15 cm long and 6 cm wide.
DThe rectangle is 17 cm long and 3 cm wide.
EThe rectangle is 16 cm long and 5 cm wide.
FThe rectangle is 14 cm long and 7 cm wide.

7. A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?
AThere are five of each type of coin in the wallet.
BThere are nine of each type of coin in the wallet.
CThere are seven of each type of coin in the wallet.
DThere are eight of each type of coin in the wallet.
EThere are six of each type of coin in the wallet.
FThere are ten of each type of coin in the wallet.

8. You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Heres the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?
AAfter borrowing 3 rock CDs, your friend will have 21 rock CDs, 12 country CDs, and 3 soundtracks.
BAfter borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and 3 soundtracks.
CAfter borrowing 3 rock CDs, your friend will have 25 rock CDs, 10 country CDs, and 4 soundtracks.
DAfter borrowing 3 rock CDs, your friend will have 21 rock CDs, 9 country CDs, and 3 soundtracks.
EAfter borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and no soundtracks.
FAfter borrowing 3 rock CDs, your friend will have 18 rock CDs, 15 country CDs, and 3 soundtracks.

9. After watching hours of those home improvement shows, you decide you want to paint you bedroom. You dont want to paint all four walls the same color (how boring!), but instead, you want to paint one wall a different color. The electric orange paint youve chosen for the "special" wall is more expensive, and youre on a budget, so you need to know the area of the wall so you can buy the smallest amount of paint possible. You know that the height of the wall is half the length. You also know that the perimeter of the rectangular wall is 48 feet. What is the area of the wall?
AThe area of the wall is 128 sq.ft.
BThe area of the wall is 116 sq. ft.
CThe area of the wall is 144 sq. ft.
DThe area of the wall is 140 sq. ft.
EThe area of the wall is 416 sq. ft.
FThe area of the wall is 136 sq. ft.

10. Your mother has left you in charge of the annual family yard sale. Before she leaves you to your entrepreneurial abilities, she explains that she has made the job easy for you: everything costs either $1.50 or $3.50. She asks you to keep track of how many of each type of item is sold, and you make a list, but it gets lost sometime throughout the day. Just before shes supposed to get home, you realize that all you know is that there were 150 items to start with (your mom counted) and you have 41 items left. Also, you know that you made $227.50. Write a system of equations that you could solve to figure out how many of each type of item you sold.
Ax + y = 109
(1.5)x + 227.50 = (3.5)y

Bx + y = 109
(3.5)x + 227.50 = (1.5)y

Cx + y = 41
(1.5)x + 227.50 = (3.5)y

Dx + y = 109
(1.5)x + (3.5)y = 227.50

Ex + y = 150
(1.5)x + (3.5)y = 227.50

Fx + y = $3.50
(1.5)x + (3.5)y = 227.50

11. The second of two numbers is 5 more than twice the first. The sum of the numbers is 44. Find the numbers by writing and solving a system of equations.
A(11, 33)
B(22, 22)
C(20, 24)
D(17, 22)
E(13,31)
F(17, 27)

12. A shipment of TV sets, some weighing 30 kg each and the other weighing 50 kg each, has a total weight of 880 kg. If there are 20 TV sets all together, how many weigh 50 kg and how many weigh 30 kg?
A6 weigh 50 kg and 14 weigh 30
B15 weigh 50 kg and 5 weigh 30 .
C2 weigh 50 kg and 18 weigh 30
D14 weigh 50 kg and 6 weigh 30
E4 weigh 50 kg and 16 weigh 30
F11 weigh 50 kg and 9 weigh 30

13. The sum of the ages of Stephanie and Heather is 46. Heather is two years younger than Stephanie. Write a system of equations to determine the ages of Stephanie and Heather.
AS + H = 46
H = S + 2

BS - H = 46
H - 2 = S

CS + H = 46
H = S - 2

DS - H = 2
H = S - 46

ES + H = 2
H = S - 46

F2S H = 46

14. A nursery owner has 288 rose bushes. There are 36 fewer red roses than pink roses. How many of each type of roses are there?
ARed roses: 162; pink roses: 252.
BRed roses: 162; pink roses: 126.
CRed roses: 99; pink roses: 126.
DRed roses: 126; pink roses: 162
ERed roses: 126; pink roses: 99
FRed roses: 252; pink roses: 162

15. Chris has a jar with nickels and quarters in it. There are 95 coins in the jar and the coins total $12.95. How many of each coin is there?
A90 quarters and 5 nickels.
B54 quarters and 41 nickels.
C46 quarters and 49 nickels.
D49 quarters and 46 nickels.
E41 quarters and 54 nickels
F5 quarters and 90 nickels.

16. A store sells televisions for $360 and DVD burners for $270. The entire stock is worth $52,920 and there are a total of 164 televisions and DVD burners combined. How many of each on are there?
A93 televisions; 72 DVD burners.
B72 televisions; 93 DVD burners.
C 96 televisions; 68 DVD burners.
D94 televisions; 74 DVD burners.
E74 televisions; 94 DVD burners
F95 televisions; 71 DVD burners.

17. The owner of an organic fruit stand also sells nuts. She wants to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound. How much of each kind of nut should she include in the mixed bag?
ACashews: 0.10 lb.; peanuts: 0.40 1b.
BCashews: 0.43 lb.; peanuts: 0.07 1b.
CCashews: 0.40 lb.; peanuts: 0.10 1b.
DCashews: 0.27 lb.; peanuts: 0.23 1b.
ECashews: 0.23 lb.; peanuts: 0.27 1b.
FCashews: 0.07 lb.; peanuts: 0.43 1b.

bobbym · 2011-07-03 07:47:48

Yikes!

zee-f · 2011-07-03 07:48:13

hey

yup they did

the sum of four times the larger and three times the smaller is 71.
4(14) + 3(5) = 71

zee-f · 2011-07-03 07:49:13

hhhhhhhhhhhhh yup am working on them hhhh

bobbym · 2011-07-03 07:50:28

What do you need?

zee-f · 2011-07-03 07:51:43

am working on them and when am doin i just need to know if what i did i correct

bobbym · 2011-07-03 07:52:26

Okay, post your answers when you get them.

zee-f · 2011-07-03 07:53:10

so far for 6 i got f

bobbym · 2011-07-03 07:54:20

F is correct!

anonimnystefy · 2011-07-03 07:54:21

hi zee-f

correct!

zee-f · 2011-07-03 07:54:31

7 i got b and am working on 8

bobbym · 2011-07-03 07:55:23

Hi;

Did that one already. B is correct.

zee-f · 2011-07-03 07:57:28

thanxx guys ill submit the rest when am done

bobbym · 2011-07-03 07:58:50

Okay, see you then.

anonimnystefy · 2011-07-03 07:59:13

ok,take your time.

Last edited by anonimnystefy (2011-07-03 07:59:30)

zee-f · 2011-07-03 08:00:48

ok so for 8 i got 8 r=21 s=3 c=12

and for 9 i got 128 a

bobbym · 2011-07-03 08:01:19

Hi;
For 8)
A is the correct answer.

For 9)

A is again correct.

zee-f · 2011-07-03 08:11:04

and i got e for 10

bobbym · 2011-07-03 08:12:00

Nope! 10 is D.

Let x be the articles you sell at 1.50

Let y be the articles you sell at 3.50

x + y = 109 ( you sold 109 articles, 150 - 41 = 109 )

1.5 x + 3.5 y = 227.50

x = 77
y = 32

Math Is Fun Forum

#126 2011-07-03 03:42:25

Re: Solving systems of equations using Substitution method and elimination

#127 2011-07-03 03:43:58

Re: Solving systems of equations using Substitution method and elimination

#128 2011-07-03 03:44:44

Re: Solving systems of equations using Substitution method and elimination

#129 2011-07-03 07:37:01

Re: Solving systems of equations using Substitution method and elimination

#130 2011-07-03 07:45:28

Re: Solving systems of equations using Substitution method and elimination

#131 2011-07-03 07:46:47

Re: Solving systems of equations using Substitution method and elimination

#132 2011-07-03 07:46:58

Re: Solving systems of equations using Substitution method and elimination

#133 2011-07-03 07:47:48

Re: Solving systems of equations using Substitution method and elimination

#134 2011-07-03 07:48:13

Re: Solving systems of equations using Substitution method and elimination

#135 2011-07-03 07:49:13

Re: Solving systems of equations using Substitution method and elimination

#136 2011-07-03 07:50:28

Re: Solving systems of equations using Substitution method and elimination

#137 2011-07-03 07:51:43

Re: Solving systems of equations using Substitution method and elimination

#138 2011-07-03 07:52:26

Re: Solving systems of equations using Substitution method and elimination

#139 2011-07-03 07:53:10

Re: Solving systems of equations using Substitution method and elimination

#140 2011-07-03 07:54:20

Re: Solving systems of equations using Substitution method and elimination

#141 2011-07-03 07:54:21

Re: Solving systems of equations using Substitution method and elimination

#142 2011-07-03 07:54:31

Re: Solving systems of equations using Substitution method and elimination

#143 2011-07-03 07:55:23

Re: Solving systems of equations using Substitution method and elimination

#144 2011-07-03 07:57:28

Re: Solving systems of equations using Substitution method and elimination

#145 2011-07-03 07:58:50

Re: Solving systems of equations using Substitution method and elimination

#146 2011-07-03 07:59:13

Re: Solving systems of equations using Substitution method and elimination

#147 2011-07-03 08:00:48

Re: Solving systems of equations using Substitution method and elimination

#148 2011-07-03 08:01:19

Re: Solving systems of equations using Substitution method and elimination

#149 2011-07-03 08:11:04

Re: Solving systems of equations using Substitution method and elimination

#150 2011-07-03 08:12:00

Re: Solving systems of equations using Substitution method and elimination

Board footer