Simone has discovered a blow-out sale in the mall. The cost of 1 sweater, 3 shirts, and 2 pairs of pants is $100. The cost of 3 sweaters and 6 pairs of pants is $201. The cost of 8 shirts and 2 pairs of pants is $144. If x is the number of sweaters, y is the number of shirts, and z is the number of pants, which system of equations can be used to determine the sale price of the sweaters, shirts, and pants?

x+3y+2z=100 3x+6z=201 8y+2z=144

x+3y+2z=100 3x+y+6z=201 x+8y+2z=144

x+3y+2z=100 3x-6z=201 8y-2z=144

Choose the correct variables for the scenario. A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children under 12 years old. A total of 278 tickets were sold for one showing with a total revenue of $1300. If the number of adult tickets sold was 10 less than twice the number of student tickets, how many of each type of ticket were sold for the showing?

a = number of adult tickets s = number of student tickets c = number of children tickets

a = cost of 6 adult tickets s = cost of 3.5 student tickets c = cost of 2.5 children tickets

a = cost of 1 adult tickets s = cost of 1 student tickets c = cost of 1 children tickets

Choose the correct equations for the scenario. A theater has tickets at $6 for adults, $3.50 for students, and $2.50 for children under 12 years old. A total of 278 tickets were sold for one showing with a total revenue of $1300. If the number of adult tickets sold was 10 less than twice the number of student tickets, how many of each type of ticket were sold for the showing?

a = 2 s − 10 a\ =\ 2s-10 a = 2 s − 1 0 a + s + c = 278 a\ +\ s\ +\ c\ =\ 278 a + s + c = 2 7 8 6 a + 3.5 s + 2.5 c = 1300 6a\ +\ 3.5s\ +\ 2.5c\ =\ 1300 6 a + 3 . 5 s + 2 . 5 c = 1 3 0 0

a = 2 s − 10 a\ =\ 2s\ -\ 10 a = 2 s − 1 0 a + s + c = 1300 a+s\ +c\ =\ 1300 a + s + c = 1 3 0 0 6 a + 3.5 s + 2.5 c = 278 6a\ +\ 3.5s\ +\ 2.5c\ =\ 278 6 a + 3 . 5 s + 2 . 5 c = 2 7 8

2 a = s − 10 2a\ =\ s\ -\ 10 2 a = s − 1 0 s + a + c = 278 s\ +\ a\ +\ c\ =\ 278 s + a + c = 2 7 8 6 s + 3.5 a + 2.5 c = 1300 6s\ +\ 3.5a\ +\ 2.5c\ =\ 1300 6 s + 3 . 5 a + 2 . 5 c = 1 3 0 0

Choose the correct equations for the scenario. Sarah buys 1 lb. of jelly beans and 2 lb. of chocolates for $2.00. She then buys 1 lb. of jelly beans and 2 lb. of licorice for $3.00. She also buys 2lb. of chocolates and 2 lb. of licorice for $2.00. How much will it cost to buy 1lb. of each of the three candies?

j + 2 c = 2 j\ +\ 2c\ =\ 2 j + 2 c = 2 2 l + j = 3 2l\ +\ j\ =\ 3 2 l + j = 3 2 c + 2 l = 2 2c\ +\ 2l\ =\ 2 2 c + 2 l = 2

j + 2 c = 3 j\ +\ 2c\ =\ 3 j + 2 c = 3 j + 2 l = 2 j\ +\ 2l\ =\ 2 j + 2 l = 2 2 j + 2 c = 2 2j\ +\ 2c\ =\ 2 2 j + 2 c = 2

c + 2 j = 2 c\ +\ 2j\ =\ 2 c + 2 j = 2 j + 2 l = 3 j\ +\ 2l\ =\ 3 j + 2 l = 3 2 c + 2 l = 2 2c\ +\ 2l\ =\ 2 2 c + 2 l = 2

Determine the Variables / Formulate the system of equations - Select the best two answers The local college's bookstore sells collegiate t-shirts, hoodies and hats. During t their Family Visit Day Sale, the bookstore made a $119 Sale consisting of three t-shirts, a hoodie, and a hat: a $76 sale consisting of two t-shirts and two hats: and a $265 sale consisting of 5 t-shirts, 3 hoodies, and 2 hats. Calculate the price of each item.

3a + b + c = 119 2a + 2c = 76 5a + 3b + 2c = 265

a = Price of a t-shirt b = Price of a hoodie c = price of a hat

3a + b + c = 76 2a + 2c = 119 5a + 3b + 2c = 265

3a + b + c = 265 2a + 2c = 76 5a + 3b + 2c = 119

a = number of t-shirts b = number of hoodies c = number of hats

Determine the Variables / Formulate the Systems of equations / Choose the best two answers. Raven has $80 in 15 bills in her pocket, including ones, tens, and twenties. If the number of one dollar bills is twice the combined number of tens and twenties, how many of each denomination does Raven have in her pocket

x = number of one dollar bills y = number of ten dollar bills z = number of twenty dollar bills

x + y + z = 15 x + 10y + 20z = 80 x = 2(y +z)

x = number of bills y = amount of money z = types of denominations

x + y + z = 15 x + 10y + 20z = 80 x = 4y + 2Z

x + y + z = 15 x + 5y + 10z = 90 x = 2(y +z)

Formulate 3 Variable Systems

Quiz

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

AII.9-12.3.A

Standards-aligned

Shannon Jenks

Used 2+ times

FREE Resource

21 questions

Show all answers

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

x + y = 1550

y = 4x

x + y = 1550

y = x + 4

y - x = 1550

y = 4x

y = 1550 + x

y = x + 4

Tags

AII.9-12.3.A

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels?

d + n = 6.60
.10d + .05n = 80

d + n = 80
d + n = 6.60

d + n = 80
.10d + .05n = 6.60

d + n = 80
.05d + .10n = 6.60

Tags

AII.9-12.3.A

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The perimeter of rectangular box is 18 inches and the width is five inches less than the length. If W=width of the box and L=length of the box, which system of equations matches the situation?

L + W = 18
W = L - 5

2L + 2W = 18
L = W - 5

2L + 2W = 18
W = L - 5

2L + 2W = 18
W = 5 - L

Tags

AII.9-12.3.A

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Erica has $14 and plans to save $5 each week until she has the $64 she needs for a new jacket. How many weeks will it take Erica to save money for a new jacket? Use w as the number of weeks.

5 + 14w = 64

14 + 5w = 64

19w = 64

5w - 14 = 64

Tags

AII.9-12.3.A

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

S + A = 530
3S + 4A = 1740

S + A = 530
4S + 3A = 1740

S + A = 1740
3S + 4A = 530

S + A = 1740
4S + 3A = 530

Tags

AII.9-12.3.A

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Two numbers have a sum of 25.
One number is five more than the other number. Find the numbers.

Which system best represents the information?

x + y = 25

x = 5 + y

xy = 25

x = 5 + y

x + y = 25

x = 5y

xy = 25

x = 5y

Tags

AII.9-12.3.A

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The sum of three numbers is 35. The product of the first number times the third number is 87. The quotient of the third number divided by the first number is 1.5. Which of the following systems of equations can be used to determine the three numbers?

x+y+z=35

xz=87

x-1.5z=0

x+y+z=35

xz=87

-1.5x+z=0

x+y+z=35

xz=87

x/z=1.5

x+y+z=35

xz=87

1.5/x=z

Tags

AII.9-12.3.A

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Choose the correct equations for the scenario.

A parking lot has spaces reserved for motorcycles, cars, and vans. There are five more spaces reserved for vans than for motorcycles. There are three times as many car spaces as van and motorcycle spaces combined. If the parking lot has 180 total reserved spaces, how many of each type are there?

m\ +\ c\ +\ v\ =\ 180

v\ =\ m\ +\ 5

c\ =\ 3\left(m\ +\ v\right)

$m\ +\ c\ +\ v\ =\ 180$
$m\ =\ v+5$
$c\ =\ 3m\ +\ v$

$c\ +\ m\ +\ v\ =\ 180$
$m\ =\ v+5$
$3c\ =\ m+v$

Tags

AII.9-12.3.A

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Formulate 3 Variable Systems

21 questions

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels?

The perimeter of rectangular box is 18 inches and the width is five inches less than the length. If W=width of the box and L=length of the box, which system of equations matches the situation?

Erica has $14 and plans to save $5 each week until she has the $64 she needs for a new jacket. How many weeks will it take Erica to save money for a new jacket? Use w as the number of weeks.

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

Two numbers have a sum of 25. One number is five more than the other number. Find the numbers.Which system best represents the information?

The sum of three numbers is 35. The product of the first number times the third number is 87. The quotient of the third number divided by the first number is 1.5. Which of the following systems of equations can be used to determine the three numbers?

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Two numbers have a sum of 25.
One number is five more than the other number. Find the numbers.

Which system best represents the information?