WorksheetsSystems of Linear Equations Word Problems
Total questions: 30
Worksheet time: 2hrs 12mins
Toby skated from his house to the beach at a constant speed of 8 kilometers per hour, and then skated from the beach to the park at a constant speed of 7 kilometers per hour. The total distance Toby skated was 20 kilometers, and it took him twice as long to get to the park.
Let b be the number of hours it took Toby to skate from his house to the beach, and p the number of hours it took him to skate from the beach to the park.
Which system of equations represents this situation?
8b + 7p = 20
b = 2p
8b + 7p = 20
p = 2b
8b + 7p = 20
b = p/2
8b + 7p = 20
p = b/2
Michael uses a blend of dark chocolate and milk chocolate to make the ice cream topping at his restaurant. He needs to buy 100 kg of chocolate in total for his next order. Dark chocolate costs $12 per kilogram, milk chocolate costs $10 per kilogram, and he wants to spend $1120 total.
Let d be the number of kilograms of dark chocolate he buys and m be the number of kilograms of milk chocolate he buys.
Which system of equations represents this situation?
d + m = 100
12d + 10m = 1120
d + m = 1120
12d + 10m = 100
d + m = 100
10d + 12m = 1120
d + m = 1120
10d + 12m = 100
Chevy has some yarn that he wants to use to make hats and scarves. Each hat uses 0.20 kilograms of yarn and each scarf uses 0.10 kilograms of yarn. Chevy wants to use 2 kilograms of yarn to make a total of 15 items.
Let h be the number of hats Chevy makes and s be the number of scarves he makes.
Which system of equations represents this situation?
0.20h + 0.10s = 2
h + s = 15
0.20h + 0.10s = 15
h + s = 2
0.10h + 0.20s = 2
h + s = 15
0.10h + 0.20s = 15
h + s = 2
Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel.
Let k be Kevin's age and let d be Daniel's age.
Which system of equations represents this situation?
k = d + 3
k - 2 = 4(d - 2)
k = d + 3
k - 2 = 4d
k = d + 3
k - 2 = 2d
k = d - 3
k - 2 = 4(d - 2)
Lucy drove from her home to the grocery store at a constant speed of 10 kilometers per hour, and then drove from the grocery store to the library at a constant speed of 5 kilometers per hour. The total distance Lucy drove was 30 kilometers, and it took her three times as long to get to the library.
Let g be the number of hours it took Lucy to drive from her home to the grocery store, and l the number of hours it took her to drive from the grocery store to the library.
Which system of equations represents this situation?
10g + 5l = 30
g = 3l
10g + 5l = 30
l = 3g
10g + 5l = 30
g = l/3
10g + 5l = 30
l = g/3
John has some clay that he wants to use to make pots and vases. Each pot uses 0.30 kilograms of clay and each vase uses 0.15 kilograms of clay. John wants to use 3 kilograms of clay to make a total of 20 items.
Let p be the number of pots John makes and v be the number of vases he makes.
Which system of equations represents this situation?
0.30p + 0.15v = 3
p + v = 20
0.30p + 0.15v = 20
p + v = 3
0.15p + 0.30v = 3
p + v = 20
0.15p + 0.30v = 20
p + v = 3
John is planning to make a fruit punch for his party. He needs 50 liters of punch in total. Orange juice costs $5 per liter, apple juice costs $4 per liter, and he wants to spend $220 in total.
Let o be the number of liters of orange juice he uses and a be the number of liters of apple juice he uses.
Which system of equations represents this situation?
o + a = 50
5o + 4a = 220
o + a = 220
5o + 4a = 50
o + a = 50
4o + 5a = 220
o + a = 220
4o + 5a = 50
Sarah is planning to make a mix of almonds and cashews for her snack. She needs 30 kg of nuts in total. Almonds cost $15 per kilogram, cashews cost $10 per kilogram, and she wants to spend $390 total.
Let a be the number of kilograms of almonds she buys and c be the number of kilograms of cashews she buys.
Which system of equations represents this situation?
a + c = 30
15a + 10c = 390
a + c = 390
15a + 10c = 30
a + c = 30
10a + 15c = 390
a + c = 390
10a + 15c = 30
John is 5 years older than Mary. Three years ago, John was 3 times as old as Mary.
Let j be John's age and let m be Mary's age.
Which system of equations represents this situation?
j = m + 5
j - 3 = 3(m - 3)
j = m + 5
j - 3 = 3m
j = m + 5
j - 3 = 2m
j = m - 5
j - 3 = 3(m - 3)
Kevin is 3 times as old as Daniel. 4 years ago, Kevin was 5 times as old as Daniel.
How old is Daniel now?
Ben is 4 times as old as Daniel and is also 6 years older than Daniel.
How old is Ben?
Ben is 21 years older than Isaac. Three years ago, Ben was 4 times as old as Isaac.
How old is Ben now?
Ben is 22 years older than Daniel. Three years ago, Ben was 3 times as old as Daniel.
How old is Daniel now?
George was selling statues of elephants and tigers. The combined height of one elephant statue and one tiger statue is 21 meters. The height of 4 tiger statues stacked on top of each other is 24 meters taller than one elephant statue.
How tall is each elephant statue?
Solve this system.
(1, -4)
(1, 4)
(-4, -7)
(-7, -4)
3x - y = 7
2x + y = 3
Solve:
−4x − 4y = 0
4x + 4y = 0
Solve:
-4x - 6y = 6
4x + 6y = -4
Solve the following system:
x = 6
y = 2x - 3
(6, 6)
(6, 9)
(9, 6)
(9, 9)
Solve the following system:
4x−3y=18
(3, −2)
(3, 2)
(−2,3)
(2, 3)
Solve the following system using any method.
y = 2/3x - 2
y = -x + 3
(0,3)
(0,-3)
(3,0)
(-3,0)
Solve the following system using any method.
3x + 2y = 16
7x + y = 19
(-2,5)
(-2,-5)
(2,-5)
(2,5)
Solve the following system using any method.
y = 2x + 1
y = 4x - 1
(1,3)
(-1,-3)
(-1,3)
(3,1)
y=8x+1
y=6x+3
Wyatt and Emerson went shopping at a back-to-school sale where all shirts and shorts were the same price. Wyatt spent $175 on 7 new shirts and 7 pairs of shorts. Emerson purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?
On the first night, Raleigh Grande sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. If I take my son, how much will I pay for tickets?
Gracie sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. She sold 21 tickets total. How many adult tickets did Gracie sell?
Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of oatmeal cookies?
Jane found a bag of quarters and dimes. She counted a total of 62 coins for a total of $12.20. How many quarters are in the bag?
