Write equations to represent situations
There are 30 students in a class. Today, 26 students are present. Write and solve an equation to show how many students are absent.
26 + x = 30
subtract 26 from both sides
x = 4
z + 8.5 = 15
z = 6.5
5x = 80
x = 16
A room in the shape of a regular octagon (an 8-sided shape) has a perimeter of 72 feet.
What is the length of each side of the room? Let s represent the length in feet of each side of the room.
Write and solve an equation for s.
8s = 72
s= 9
James spent no more than $20 at the mall. Write an inequality to represent how much James spent.
x ≤ 20
There are 12 trees on the Smiths’ property. The Smiths plant some trees, and now there are 21 trees. How many trees t do the Smiths plant? Write an equation to find the number of trees that are planted.
12 + t = 21
x - 4.8 = 2.4
x = 7.2
q/4 = 12
q = 48
Maisie is watching a movie. She has been watching for 36 minutes. There are 55 minutes to go. How long does the movie last? Let m represent the number of minutes that the movie lasts. Write and solve an equation for m.
m - 36 = 55
add 36 to both sides
m = 91
According to government guidelines, drones may not fly higher than 400 feet. Write and inequality that is true only for the height a drone can fly above the ground.
x ≤ 400
Lizzie goes to the Lakeside Mall with friends. She spends $25 and returns home with $45. How much money d in dollars does Lizzie start with?
Write an equation to find the amount of money Lizzie starts with.
d - 25 = 45
Joe has 24 songs on a playlist. He decides to increase the playlist, and it now has 32 songs. How many new songs does Joe put on his playlist?
24 + s = 32
subtract 24 from each side of the equation
s = 8
⅔x = 18
x = 27
The area of a rectangle is found by using the formula
A = l × w,
where A is the area, l is the length, and w is the width.
A rectangular desktop has an area of 18 square feet. The length of the desk is 6 feet. What is the width of the desktop? Write and solve an equation for w.
A = l x w
18 = 6w
divide both sides by 6
w = 3
At an amusement park, people must be at least 4.8 feet to ride the ferris wheel. Write an inequality that shows the heights of people who may ride the ferris wheel.
x ≥ 4.8
A test is 45 minutes long. There are 3 sections of the test that each take an equal amount of time. How many minutes m is each section of the test?
Write an equation to find the number of minutes for each section.
3m = 45
Adrianne is reading a book. She reads 275 pages and has 155 pages to go.
How many pages p is Adrianne’s book? Write and solve an equation to find the book’s length in pages.
p - 275 = 155
or
p - 155 = 275
p = 430
Yasmine earns $54 for dog-walking. She walks her neighbor’s dog 12 times.
A. Write an equation to represent how to find the amount Yasmine earns per dog walk. Explain what your variable represents.
12x=54
the variable, x, represents the amount she earns for one dog walk.
Sam has 36 pieces left to complete a puzzle. He has already put together 414 pieces. How many pieces p are in the puzzle? Write and solve an equation for p.
p - 414 = 36
add 414 to both sides
p = 450
When cooking a turkey, the recommended internal temperature of the turkey is 165 °F. A lower internal temperature will undercook the turkey.
Write an inequality that is true only for temperatures t at which the turkey will be undercooked.
t < 165
Mike bakes 24 cookies for some friends. He gives the same number of cookies to 2 friends. How many cookies c does each friend receive? Write an equation to find the number of cookies each friend receives.
2c =24
Zoe buys a magazine for $5.75. She gives the cashier a $10 bill. If Zoe receives the correct change, how much change c in dollars will she receive?
Write and solve an equation to find the correct change.
c + 5.57 = 10
subtract 5.57 from each side of the equation
c= $4.43
Mr. Folsom buys 8 boxes of ice pops. There are the same number of ice pops in each box. There are 96 ice pops in all. How many ice pops are in each box?
8p = 96
divide each side by 8
p = 12
Five pounds of cherries cost $14.95. Write and solve an equation to determine how much each pound of cherries costs.
5x = 14.95
divide each side by 5
x = $2.99
A commercial jet travels at 885 kilometers per hour. Engineers have designed other aircraft to travel even faster. Write an inequality that is true only for speeds s of these other aircraft.
s > 885