Word Problems
Jack and Ming are selling pies for a school fundraiser. Customers can buy apple pies and pumpkin pies. Jack sold 12 apple pies and 12 pumpkin pies for a total of $228. Ming sold 6 apple pies and 2 pumpkin pies for a total of $54. What is the cost each of one apple pie and one pumpkin pie?
x= Cost of 1 apple pie
y= Cost of 1 pumpkin pie
12x+12y=228
6x+2y=54
By graphing, the solution to the system
y = x
y = -x
What is (0,0) ?
The solution to the system
x + y = 2
y = 3
What is (-1,3) ?
The solution to the system
x + 5y = 12
-x +y = 0
What is (2,2) ?
(4,5) is the solution to the following system?
4x - y = 12
x + 6y = 13
What is, NO ?
Natalie and Emily each improved their yards by planting rose bushes and ivy. They bought their supplies from the same store. Natalie spent $60 on 4 rose bushes and 4 pots of ivy. Emily spent $148 on 8 rose bushes and 12 pots of ivy. What is the cost of one rose bush and the cost of one pot of ivy?
x= Cost of 1 rose bush
y= Cost of 1 pot of ivy
4x+4y=60
8x+12y=148
By graphing, the solution to the system
y = 3x - 4
y = -3x + 2
What is (1,-1)?
x = 2y - 4
10y - x = 20
What is (0,2) ?
The solution to the system
-4x - 2y = -12
4x + 8y = -24
What is (6,-6)?
(0,-4) the solution to the system
y = -20x + 1
20x + y = 6
What is No?
John went to Yellow Stone National Park one day this summer. All of the people in the park were either buying water or ice cream. Ice cream costs $3 and water costs $1.50. If there were a total of 167 people at the park that spent $712, how many ice creams and waters were sold?
x= Number of ice creams sold
y= Number of waters sold
x+y=167
3x+1.5y=712
By graphing, the solution to the system
y = (1/3)x + 2
y = -x - 2
What is (-3,1) ?
The solution to the system
y = 6x - 11
-2x - 3y = -7
What is (2,1) ?
The solution to the system
5x + y = 9
10x - 7y = -18
What is (1,4)?
(-2,1) is a solution to the system
6x - 3y = -15
2x + y = -3
What is Yes?
Harold had a summer lemonade stand where he sold small cups of lemonade for $1.25 and large cups for $2.50. If Harold sold a total of 155 cups of lemonade and collected a total of $265, how many cups of each type did he sell?
x= Number of small cups of lemonade sold
y= Number of large cups of lemonade sold
x+y=155
1.25x+2.5y=265
By graphing, the solution to the system
y = -(3/2)x - 4
y = (1/2)x + 4
What is (-4,2) ?
The solution to the system
-3x + 3y = 4
y = 3 +x
What is no solution?
The solution to the system
-4x + 9y = 9
x - 3y = - 6
What is (9,5)?
No solution describes the solution to the following system
y = 3x + 4
y = -x - 4
What is No?
Phil bought 6 new compact disks and 2 used compact disks for $127.92. At the same prices, Mackenzie bought 3 new compact disks and 8 used compact disks for $133.89. Find the cost of buying a single used compact disk and a single new compact disk.
x= Cost of 1 new compact disk
y= Cost of 1 used compact disk
6x+2y=127.92
3x+8y=133.89
By graphing, the solution to the system
y = (5/4)x - 2
y = (5/4)x -1
What is no solution?
The solution to the system
4x + 2y = -12
y = -2x - 6
What is infinitely many solutions
The solution to the system
2x + 8y = 6
-5x - 20y = -15
What is infinite number of solutions?
(-3,-1) is the solution to
y=(4/3)x + 3
(2/3)x + y = -3
What is Yes?