Word Problems
The amount of money each child received when Mr. Vogel left $25,000 divided between his son and daughter, with the daughter receiving $5000 less than the son.
$15,000 for son
$10,000 for daughter
Use substitution to solve the system of equations.
`y=x-1`
`x+y=7`
(4,3)
Use elimination to solve
`3x+2y=4`
`4x-2y=-18`
(-2,5)
y+x=5
3x-5y=-1
3,2
How many solutions does the following system have?
`21x-6y=54`
`9+y=3x5x`
Infinitely many
Solve the inequality in interval notation
`|3x-9|<27`
x<12
(-6,12)
x>-6
A shopper bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660. What was the cost of one shirt?
The solution to the system
y = x - 2
3x - y = 16
(7,5)
Use elimination to solve
`3x+5y=-16`
`2x+3y=-9`
(3,-5)
The solution to the system of equations:
y = -3
x = 5
(5,-3)
In the system of equations below, q is a constant. If the system has infinitely many solutions, what is the value of q?
`6x+3y=18`
`qx-y/3=-2`
`-2/3`
`|(x-2)/5|+2>12`
(-infinity,-48) and (52,infinity)
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
solve the system of equations using substitution
2x-y=2
3x-2y=11
(-7, -16)
Solve the system
2a - 4b = 12
-8a + 16b = -48
Infinitely many solutions
y-x=0
8x+4y=-24
-2, -2
What is the sum of x and y?
3x-3y=0
y=2x+5
-10
`|(3x-4)|/-5-4<3`
All real numbers
What are the dimensions of a rectangle whose perimeter is 78 inches, when the length of the rectangle is twice its width?
26 inches by 13 inches
solve using substitution
y=3x+5
x=-3y-5
-2, -1
y=10-x
3x-3y=0
5,5
12x-3y=-15
8x+8y=-58
-2.45, -4.8
A sofa costs $50 less than three times the cost of a chair. If the sofa and chair together cost $650, how much more does the sofa cost than the chair?
$300
`|x^2|/-2>5`
no solution
A zookeeper needs to mix feed for the prairie dogs so that the feed has the right amount of protein. Feed A has 12% protein. Feed B has 5% protein. How many pounds of each does he need to mix to get 100lb of feed that is 8% protein?
42.9 lb of feed A
57.1 lb of feed B
If
`y=-x-15`
and
`(5y)/2-37=-x/2`
then what is the value of
`2x+6y?`
59
The solution to the system:
`1/3x + 1/4y = 10`
`1/3x - 1/2y = 4`
(24,8)
solve by graphing the system of equations
y=3x-3
y=3x+1
The system of equations has how many solutions
21x-6y=54
9+y=3.5x
infinitely many