Seasonal System of Equations
Solve each problem using a system of equations and write your answer as an
ordered pair. Solve each system using any algebraic method: substitution, or
elimination.
1. It takes Jack Frost 5 minutes to fly 35 miles with the wind. It takes him 7
minutes to go 35 miles against the wind. Determine his speed in still air (x) and the
speed of the wind (y).
Ordered Pair M:_______________
2. The Easter bunny made 13 eggs one day. Some were yellow and the rest were purple.
The number of purple eggs he made was one more than twice the number of yellow
eggs. How many yellow eggs (x) and purple eggs (y) did the Easter bunny make?
Ordered Pair E:_______________
3. After a big snow storm, Tim and Tom decided to shovel driveways for money. Tom
shoveled 3 less than twice as many driveways as Tim. They shoveled a total of 15
driveways. How many driveways did Tim (x) and Tom (y) each shovel?
Ordered Pair I:_______________
4. Your high school is having a competition where students have to guess how many jelly
beans are in a jar. The tens digit is 4 more than twice the ones digit. The sum of the
digits is 4. How many jelly beans are in the jar? Find the tens digit (x) and the ones digit
(y).
Ordered Pair O:______________
5. Cathy and Vicky go shopping for gift wrap one day. Cathy buys 3 rolls of wrapping paper
and 5 bows for a total of $32. Vicky gets 1 roll of wrapping paper and 2 bows for $11.
How much does each roll of wrapping paper (x) and each bow (y) cost?
Ordered Pair L:______________
6. Scarves and socks are on sale at the store! One woman was able to buy 5 scarves and 4
pairs of socks for $30. Another woman purchased 3 pairs of socks and 2 scarves for $19.
Find the price of one scarf (x) and one pair of socks (y).
Ordered Pair D:________________
7. Cassie got 3 times as many gifts as Oscar. Together Cassie and Oscar got a total of 12
gifts. How many gifts did Cassie (x) and Oscar (y) each get?
Ordered Pair F:_________________
8. Mallory and Alex each drank a cup of hot chocolate after playing in the snow. Mallory
put 6 more marshmallows in her cup than Alex. Together Mallory and Alex had a total of
6 marshmallows. How many marshmallows did Mallory (x) and Alex (y) each have in
their hot chocolate?
Ordered Pair N:_______________
9. Bobby’s grocery list had 3 more than twice as many items on it than Emily’s list. Emily
has 8 fewer items on her list than Bobby. How many items were on Emily’s (x) and
Bobby’s (y) grocery lists?
Ordered Pair G:_______________
10. Adrienne has two different bookshelves in her apartment. The taller bookshelf is 1 foot
shorter than 5 times the height of the smaller bookshelf. If she stacked the shorter
bookshelf on top of the taller bookshelf, they would be a total of 60 inches tall. Find the
heights in feet of the taller bookshelf (x) and the shorter bookshelf (y).
Ordered Pair A:_______________
11. Ballard got 2 feet less than twice the amount of snow Bellevue got. Ballard got 3 feet
more snow than Bellevue. How many feet of snow did Ballard (x) and Bellevue (y) each
get?
Ordered Pair J:________________
12. A 32 year old mother realized that her age is twice the sum of her two children’s ages.
Her son, Miles is two years older than her daughter, Amelia. How old are Amelia (x) and
Miles (y)?
Ordered Pair H:________________
13. Two families go ice skating one day. The first family spends $25 on
skate rentals for 5 kids and 2 adults. The second family spends $14
on skate rentals for 3 kids and 1 adult. How much does each child’s
skate rental (x) and each adult’s skate rental (y) cost?
Ordered Pair C:______________
14. At Fred’s house, George ate the same number of sugar cookies and chocolate chip
cookies. Twice the number of sugar cookies he ate decreased by one equals the number
of chocolate chip cookies he ate. How many sugar cookies (x) and chocolate chip cookies
(y) did George eat at Fred’s house?
Ordered Pair B:_____________
15. Mike built a rectangular snow fort with a perimeter of 24 feet.
The length of the fort was 8 feet less than 3 times the width. What was
the length (x) and width (y) of the fort?
Ordered Pair K:______________
Answer Key
1. 5(x + y) = 35
7(x – y) = 35
M = (6, 1)
2. x + y = 13
y = 2x + 1
E = (4, 9)
3. x + y = 15
y = 2x – 3
I = (6, 9)
4. x + y = 4
x = 2y + 4
O = (4, 0)
5. 3x + 5y = 32
x + 2y = 11
L = (9, 1)
6. 5x + 4y = 30
2x + 3y = 19
D = (2, 5)
7. y = 3x
x + y = 12
F = (3, 9)
8. x + y = 6
x=y+6
N = (6, 0)
9. y = 2x + 3
x=y-8
G = (5, 13)
10. x + y = 5
x = 5y – 1
A = (4, 1)
11. x = 2y – 2
x=y+3
J = (8, 5)
12. 2(x + y) = 32
y=x+2
H = (7, 9)
13. 5x + 2y = 25
3x + y = 14
C = (3, 5)
14. x = y
2x – y = 1
B = (1, 1)
15. 2x + 2y = 24
x = 3y - 8
K = (7, 5)