Solving systems of equations using Substitution method and elimination

zee-f · 2011-06-29 10:31:05

yup am working on some but am ganna do them tomorrow
1. The sum of two numbers is 90. Their difference is 18. Find the numbers.
A (40, 22)
B (45, 45)
C (36, 54)
D (27, 63)
E (40, 50)
F(72, 90)
2. The number of girls at a small high school is 60 greater than the number of boys. If there are 1250 total students, how many girls are there?
A625
B655
C705
D635
E725
F675

3. In three more years, Miguels grandfather will be six times as old as Miguel was last year. When Miguels present age is added to his grandfathers present age, the sum is 68. How old is each one now?
AMiguel is 14 and his grandfather is 54.
BMiguel is 10 and his grandfather is 58.
CMiguel is 5 and his grandfather is 63.
DMiguel is 7 and his grandfather is 61
EMiguel is 11 and his grandfather is 57.
FMiguel is 6 and his grandfather is 62.
'
4. Twice the larger of two numbers is three more than five times the smaller. The sum of four times the larger and three times the smaller is 71. What are the numbers?
AThe larger number is 12 and the smaller number is 7.
BThe larger number is 17 and the smaller number is 8.
CThe larger number is 20 and the smaller number is -3.
DThe larger number is 14 and the smaller number is 5.
EThe larger number is 24 and the smaller number is 8.
FThe larger number is 8 and the smaller number is 7.

5. Three times the width of a certain rectangle exceeds twice its length by two inches. Four times its length is twelve more than its perimeter. Write a system of equations that could be used to solve this problem. (hint: P = 2L + 2W)
A3W = 2L + 2
2L = 2W + 12

B3W + 2 = 2L
4L = P 12

C3W = 2L + 2
4L + 12 = P

D2W + 2 = 2L
4L = 12 + P

E3W + 2 = 2L
4L = 12 + P

F2L 2 = 3W
P = 4L - 12

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?
A 6 weigh 50 kg and 14 weigh 30
B 15 weigh 50 kg and 5 weigh 30 .
C 2 weigh 50 kg and 18 weigh 30
D 14 weigh 50 kg and 6 weigh 30
E 4 weigh 50 kg and 16 weigh 30
F 11 weigh 50 kg and 9 weigh 30

bobbym · 2011-06-29 14:40:43

Hi;

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?

p = n
n = d

So the answer is B

zee-f · 2011-06-30 09:21:50

i got c for number one and b for 2 am really confused on 3 i think its (A)

bobbym · 2011-06-30 09:31:06

Hi;

You are correct on 1 and 2.

You are incorrect on 3.

anonimnystefy · 2011-06-30 09:38:43

hi zee-f

your answer for 1 and 2 is correct.and if i calculated it correctly it should be E.
first try to set an equation for first part of the text.
then set one for the second part.
then solve like a system of equations.
if you get stuck somewhere just ask.

zee-f · 2011-06-30 09:44:57

thanx

anonimnystefy · 2011-06-30 09:47:43

yw

bobbym · 2011-06-30 10:56:32

Hi;

Call g the grandfathers age right now and m, Miguels age right now.

Now your two eqautions look like this.

Subtract the top one from the bottom that will make g disappear.

So m is 11.

zee-f · 2011-07-01 08:09:02

thanx guys

ok so i submitted my work for the elimination and the substitution method to my online course and my teacher asked me the following i was wondering if any body can see if i answered right

#4. What is your ordered pair?

#4- X=-4 Y=0
(-4,0)

#5. How can you simplify x + 2x?
#5- YES I CAN IT WOULD BE 3X
my ordered pairs are (1,2)

#6.What does it mean when you have 3 = -6?
#6-it means there's no solution
#8. WHat is your ordered pair?
#8-am confused on my ordered pair here

#9 What does it mean when you get 0 = 0?
#9- it means its one line

#10. What is your ordered pair?
#10-(3,7)
#14. What does y equal?
#14-confused?????????
#16. What is the ordered pair?
#16-(2,-3)

#17. What is the ordered pair?
#17-(-2,-4)
#18. What does it mean when you get 12y = 12y?
#18- it means one line

zee-f · 2011-07-01 08:52:15

ordered pair of the like equation like the x and y i think i was confused to

anonimnystefy · 2011-07-01 09:03:27

hi zee-f

number 4,5,6 are correct.8 is (-2,-4).9 is correct.10 is incorrect,it should be (13/5,7/5).as for 14 y=2.16,17 and 18 are also correct.

zee-f · 2011-07-01 09:08:35

thanx alot

anonimnystefy · 2011-07-01 09:09:49

yw

zee-f · 2011-07-01 09:45:57

anonimnystefy · 2011-07-02 00:01:19

hi zee-f

when you have time you can check out this link:http://www.mathisfunforum.com/viewtopic.php?id=4397

Last edited by anonimnystefy (2011-07-02 00:01:44)

zee-f · 2011-07-03 03:01:49

ok i will thanx )
i was wondering if anybody can help me do the question i need the equation and ill solve it thanx

bobbym · 2011-07-03 03:03:48

What question?

zee-f · 2011-07-03 03:04:57

1. The sum of two numbers is 90. Their difference is 18. Find the numbers.
A(40, 22)
B(45, 45)
C(36, 54)
D(27, 63)
E(40, 50)
F(72, 90)
2. The number of girls at a small high school is 60 greater than the number of boys. If there are 1250 total students, how many girls are there?
A625
B655
C705
D635
E725
F675
3. In three more years, Miguels grandfather will be six times as old as Miguel was last year. When Miguels present age is added to his grandfathers present age, the sum is 68. How old is each one now?
AMiguel is 14 and his grandfather is 54.
BMiguel is 10 and his grandfather is 58.
CMiguel is 5 and his grandfather is 63.
DMiguel is 7 and his grandfather is 61
EMiguel is 11 and his grandfather is 57.
FMiguel is 6 and his grandfather is 62.
4. Twice the larger of two numbers is three more than five times the smaller. The sum of four times the larger and three times the smaller is 71. What are the numbers?
AThe larger number is 12 and the smaller number is 7.
BThe larger number is 17 and the smaller number is 8.
CThe larger number is 20 and the smaller number is -3.
DThe larger number is 14 and the smaller number is 5.
EThe larger number is 24 and the smaller number is 8.
FThe larger number is 8 and the smaller number is 7.
5. Three times the width of a certain rectangle exceeds twice its length by two inches. Four times its length is twelve more than its perimeter. Write a system of equations that could be used to solve this problem. (hint: P = 2L + 2W)
A3W = 2L + 2
2L = 2W + 12

B3W + 2 = 2L
4L = P 12

C3W = 2L + 2
4L + 12 = P

D2W + 2 = 2L
4L = 12 + P

E3W + 2 = 2L
4L = 12 + P

F2L 2 = 3W
P = 4L - 12

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

bobbym · 2011-07-03 03:06:35

Hi;

I am sure I did 3 or 4 of them already. Do you have any specific one other than those?

zee-f · 2011-07-03 03:07:37

hey

yup from #5 i just need the equation and ill solve it

bobbym · 2011-07-03 03:10:32

Hi;

A is the correct system of equations. You should get L = 20 and W = 14

zee-f · 2011-07-03 03:33:52

like i ment before solving i wanted like the equation

bobbym · 2011-07-03 03:35:59

Hi;

I told you it was A)

3W = 2L + 2
2L = 2W + 12

Can you solve those?

zee-f · 2011-07-03 03:39:35

are those for #5?

bobbym · 2011-07-03 03:41:51

Yep and I even have provided you with the answer if you get stuck.

Math Is Fun Forum

#101 2011-06-29 10:31:05

Re: Solving systems of equations using Substitution method and elimination

#102 2011-06-29 14:40:43

Re: Solving systems of equations using Substitution method and elimination

#103 2011-06-30 09:21:50

Re: Solving systems of equations using Substitution method and elimination

#104 2011-06-30 09:31:06

Re: Solving systems of equations using Substitution method and elimination

#105 2011-06-30 09:38:43

Re: Solving systems of equations using Substitution method and elimination

#106 2011-06-30 09:44:57

Re: Solving systems of equations using Substitution method and elimination

#107 2011-06-30 09:47:43

Re: Solving systems of equations using Substitution method and elimination

#108 2011-06-30 10:56:32

Re: Solving systems of equations using Substitution method and elimination

#109 2011-07-01 08:09:02

Re: Solving systems of equations using Substitution method and elimination

#110 2011-07-01 08:52:15

Re: Solving systems of equations using Substitution method and elimination

#111 2011-07-01 09:03:27

Re: Solving systems of equations using Substitution method and elimination

#112 2011-07-01 09:08:35

Re: Solving systems of equations using Substitution method and elimination

#113 2011-07-01 09:09:49

Re: Solving systems of equations using Substitution method and elimination

#114 2011-07-01 09:45:57

Re: Solving systems of equations using Substitution method and elimination

#115 2011-07-02 00:01:19

Re: Solving systems of equations using Substitution method and elimination

#116 2011-07-03 03:01:49

Re: Solving systems of equations using Substitution method and elimination

#117 2011-07-03 03:03:48

Re: Solving systems of equations using Substitution method and elimination

#118 2011-07-03 03:04:57

Re: Solving systems of equations using Substitution method and elimination

#119 2011-07-03 03:06:35

Re: Solving systems of equations using Substitution method and elimination

#120 2011-07-03 03:07:37

Re: Solving systems of equations using Substitution method and elimination

#121 2011-07-03 03:10:32

Re: Solving systems of equations using Substitution method and elimination

#122 2011-07-03 03:33:52

Re: Solving systems of equations using Substitution method and elimination

#123 2011-07-03 03:35:59

Re: Solving systems of equations using Substitution method and elimination

#124 2011-07-03 03:39:35

Re: Solving systems of equations using Substitution method and elimination

#125 2011-07-03 03:41:51

Re: Solving systems of equations using Substitution method and elimination

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