Word Problems
Describe the visual representation of the each of the three solution options on a graph.
One: the lines intersect at one point (the solution)
None: the lines are parallel (same slope, different intercept)
Infinite: the lines completely overlap (same everything)
Solve the systems of equations:
y = 10x + 17
5x -3 = y
(-4, -23)
The solution to the system
2a - 4b = 12
-8a + 16b = -48
Infinitely many solutions
x = 4y
2x + 3y = 22
The grade level Ms. Poppleton is joining for snow shoeing.
6th
At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook is $8 more than 3 times the price of the novel, how much is the cost of each book? Set up and solve.
m+n =54 and m=3n+8 (let m=math and n=novel)
n=$11.50 and m=$42.50
Solve the system of equations:
3x - y = 5
y = x + 19
(7,26)
The solution to the system of equations:
y + x = 156
y - x = 27
(64.5, 91.5)
y = x - 2
3x - y = 16
The number of siblings Ms. Poppleton has.
2
The perimeter of a rectangular wooden deck is 90 feet. The deck's length is 5 feet less than 4 times its width. Set up and solve for the length and width of the deck, then calculate the area.
2L+2W=90 and L=4W-5 (let L=length and W=width)
L=35ft and W=10ft
Area = 350 square feet
Solve the system of equations:
y = -2x + 22
y = 3x - 28
(10,2)
The solution to the system:
2x + 3y = 6
3x + 5y = 15
(-15, 12)
Solve the system of equations:
-3x + 3y = 4
3 = -x + y
No solution
The grade Ms. Poppleton skipped
5th
Billy went to the fun park. He rode the water slide 5 times and the Ferris wheel twice. He spent $20 on the rides. Jenny rode the water slide 3 times and the Ferris wheel 3 times. Jenny spent $21 on rides. How much does it cost to go on the water slide?
5w+2f=20 and 3w+3f=21 (let w=waterslide and f=ferris wheel)
w=2 and f=5
Solve the system of equations:
5x + 12y = 11
3y = 4x + 1
(1/3, 7/9)
Solve the systems of equations:
10x - 9y = 46
-2x + 3y =10
(19,16)
The solution to the system:
-5x + y = -3
3x - 8y = 24
(0,-3)
The number of books Ms.Poppleton read in 2023
73
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? Set up and solve.
6s+8h=700 and 9s+6h=600 (let s=shirt and h=hat)
s=$30 and h=$65
Solve the system of equations:
c = 4b + 1
0.12b + 0.1c = 2.19
(4_1/52, 17_1/13)
Solve the systems of equations:
−1/10a+1/2b=4/5
1/7a+1/3b=−2/21
(-3,1)
The solution to the system
4e + 2f = 4
6e = f + 8
(1.25, -0.5)
The coolest gift Ms. Poppleton got over break.
What is a personalised book embosser.