Word Problems
There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?
6 chickens and 7 pigs
By graphing, the solution to the system
y = x
y = -x
(0,0)
The solution to the system
x + y = 2
y = 3
(-1,3)
The solution to the system
x + 5y = 12
-x +y = 0
(2,2)
(4,5) is the solution to the following system?
4x - y = 12
x + 6y = 13
NO !
Find the value of two numbers if their sum is 12 and their difference is 4.
(8,4)
By graphing, the solution to the system
y = 3x - 4
y = -3x + 2
(1,-1)
2y - x = 4
10y - x = 20
(4,2)
The solution to the system
-4x - 2y = -12
4x + 8y = -24
(6,-6)
(0,-4) the solution to the system
y = -20x + 1
20x + y = 6
No
John went to Yellow Stone National Park one day this summer. All of the people at the park were either hiking or bike riding. There were 178 more hikers than bike riders. If there were a total of 676 people at the park, how many were hiking and how many were riding their bikes?
427 hikers and 249 bikers
By graphing, the solution to the system
y = (1/3)x + 2
y = -x - 2
(-3,1)
The solution to the system
y = 6x - 11
-2x - 3y = -7
(2,1)
The solution to the system
5x + y = 9
10x - 7y = -18
(1,4)
(-2,1) is a solution to the system
6x - 3y = -15
2x + y = -3
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?
98 small cups and 57 large cups of lemonade
By graphing, the solution to the system
y = -(3/2)x - 4
y = (1/2)x + 4
(-4,2)
The solution to the system
-3x + 3y = 4
-x + y = 3
no solution
The solution to the system
-4x + 9y = 9
x = 3y - 6
(9,5)
No solution describes the solution to the following system
y = 3x + 4
y = -x - 4
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.
9.99
By graphing, the solution to the system
y = (5/4)x - 2
y = (5/4)x -1
no solution
The solution to the system
-5x - 8y = 17
2x - 7y = -17
(-5,1)
The solution to the system
2x + 8y = 6
-5x - 20y = -15
infinite number of solutions
(-3,-1) is the solution to
y=(4/3)x + 3
(2/3)x + y = -3
(-3,-1)