X/Y Tables
The difference of two numbers is 15. Five times the smaller number is the same as 9 less than twice the larger number. Find the numbers
x = 7
y = 22
3x + 5y = 13
2x + y = 4
x = 1
y = 2
x - 2y = 9
3x + 2y = 11
x = 5
y = -2
x = 9 - 2y
x + 3y = 16
x = -5
y = 7
Molly is throwing a beach party. She still needs to buy beach towels and beach balls. Towels are $3 each and beachballs are $4 each. She bought 10 items in total and it cost $34. How many beach balls and how many towels did she get?
4 beach balls, 6 towels
The larger of two numbers is 11 more than twice the smaller number. The sum of the numbers is 1 less than seven times the smaller number. Find the numbers.
DOUBLE JEOPARDY
x = 3
y = 17
2x + 5y = 19
y = 3x - 3
x = 2
y = 3
7x + 2y = 45
5x + y = 37
x = 7
y = 2
y = x + 5
3x + y = 25
x = 5
y = 10
Tom is buying books and notebooks for school. Books cost $15 each and notebooks cost $3 each. He bought 12 items in total and it cost $120. How many notebooks and how many books did he buy?
5 notebooks, 7 books
Jamie worked 8 hours and Bryce worked 10 hours. Their combined pay was $80. When Jamie worked 9 hours and Bryce worked 5 hours, their combined pay was $65. Write and solve a system of equations for this information by creating a table.
Jamie earned $5 per hour,
Bryce earned $4 per hour
x - 2y =-13
4x + 2y = 18
DOUBLE JEOPARDY
x = 1
y = 7
2x + y = 15
3x - y = 5
x = 4
y = 7
y = -9x - 10
y = -5x - 2
x = - 2
y = 8
A toy store sells action figures for $15 each and toy cars for $5 each. In the first sale of the day, 10 items were sold, and the price was $110. How many of each type of item was sold?
DOUBLE JEOPARDY
6 action figures, 4 toy cars
A group of 28 people attended the field trip. The number of teachers on the field trip was 20 less than the number of students. Write and solve a system of equations that describes the number of teachers, t, and the number of students, s, on that went on the field trip.
students = 24
teachers= 4
-3x - 8y = 20
-5x + y = 19
x = -4
y = -1
12x v- 9y = 37
8x + 9y = 23
x = 3
y = -1/9
-x + y = 6
4x + y = -9
x = -3
y = 3
A geometry teacher has a set of 60 plastic pentagons and octagons. She happened to notice that all the figures together have a total of 354 sides. How many of each shape are there?
42 pentagons, 18 octagons
A total of 24 students are in Alfred's class. The number of girls in the class is 3 more than twice the number of boys. Write and solve a system of equations that can be used to find the number of girls and boys who are in Alfred's class.
girls = 17
boys=7
y = 1/2x + 14
2x - 2y = -36
x = -8
y = 10
-8x - 3y = -27
-5x - 2y = -18
x = 0
y = 9
-5x + y = 1
y = -3x - 15
x = -2
y = -9
In Lewis Carroll's Through the Looking Glass, Tweedledum says, "The sum of your weight and twice mine is 361 pounds." Then Tweedledee says, "The sum of your weight and twice mine is 362 pounds." Find the weights of Tweedledum and Tweedledee.
Tweedledum is 120 pounds, Tweedledee is 121 pounds