Writing & Solving Equations
An orchard sells p pounds of apples and records the money taken in, m. The equation to calculate the value of m is m = 1.50p. If the orchard takes in $15.00, how many pounds of apples did it sell?
10 pounds of apples
Write an inequality to represent this statement: Together, the 5th grade teachers drink more than 24 cups of coffee per week.
x (or any variable) > 24
In a baker's recipe, a certain number cups of batter make a certain number of pancakes. Identify which variable is independent and which variable is dependent in this situation.
Independent: batter
Dependent: pancakes
Is n = 5 a solution to 7n = 45? Show your work using substitution to prove your answer.
No
Work must be shown with substitution - 7x5 does not equal 35
What state did Ms. Lesser live in before moving to Open Window School?
Colorado
You have the equation 12b = 24. What is the first step you need to take to solve for b?
Divide both sides by 12 / Division Property of Equality
A long jumper qualifies for the finals if they jump at least 18 feet. Write an inequality to represent this situation. If a jumper jumps exactly 18 feet, do they qualify?
x > 18
At least = greater than or equal to, so yes, a jumper jumping 18 feet would qualify
A bike shop rents out mountain bikes for $30 per day. Write an equation relating the total cost to rent c to the number of days rented d.
c = 30d
The temperature (t) was 20 degrees F at 8 am and increased by 3 degrees F each hour. Write an equation t = ... to find the temperature h hours after 8 am.
t = 20 + 3h
What did Ms. Lesser say her first name should be in order to create the greatest math teacher name of all time?
Greta (e.g. Greta Lesser, greater or lesser)
A 6-foot piece of fruit snack is cut into two pieces. If the longer piece is x feet long and the shorter piece is 1.5 feet long, write and solve an addition equation to find the length of the longer piece.
1.5 + x = 6
x = 4.5 feet
When graphing x > 5 and x > 5, what is the specific visual difference on the number line? Explain what that difference represents.
For > sign: open dot
For > sign: closed dot
The difference represents the fact that "greater than or equal to" INCLUDES the number dotted on the number line, while the "greater than" sign alone does not.
Look at this pattern:
When x = 1, y = 10
When x = 2, y = 16
When x = 3, y = 22
When x = 4, y = 28
Write an equation that represents the relationship between x and y. (In this case, plugging in the x value should result in the y value)
y = 6x + 4
A company’s supplies cost $5, and they sell decorations for $2 each. Write and solve an equation to find how many they must sell to make a profit of exactly $15.
p = 2d - 5 (or other letters)
Exactly 10 decorations must be sold to profit exactly $15.
Mr. Chatterjee has lived in three US states for over three months. One of them is Washington. Name one of the other two.
North Carolina OR California
Merijoy and George are arguing over the equation y - 12 = 30. Merijoy wants to add 12 to both sides to solve for y; George wants to subtract 5 from both sides. Explain why both are technically "correct" regarding equality, but only one helps solve for y.
They can both make these moves due to the Properties of Equality: Merijoy is using the Addition Property of Equality; George is using the Subtraction one. However, Merijoy's action will actually give an answer: y = 42. Meanwhile, George's will just result in y - 17 = 25, which while valid, doesn't help us solve for y.
How many solutions does the inequality x > 12 have? Is it possible to list them all? Why or why not?
Infinite solutions
A professional cyclist rides 27 yards in 2 seconds and 67.5 yards in 5 seconds. Assuming the speed over distance stays the same, find the pattern and predict how far the cyclist will travel in 8 seconds.
y = 13.5s, so in 8 seconds, the cyclist will travel 108 yards.
DAILY DOUBLE: THIS ONE IS EXTRA DIFFICULT! Without solving, which equation has a greater solution for x: 5x/8 = 2.75, or 5x/9 = 2.75? Justify your thinking.
5x/9 is smaller than 5x/8 because the denominator is bigger. Since you are using inverse operations to solve, you will have to multiply smaller numbers by bigger numbers to solve, making 5x/9 bigger. (Ex: imagine solving 2x = 100 vs 100x = 100. 2x is smaller than 100x, yet has a much bigger solution)
Mr. Chatterjee is currently working on his masters degree. Ms. Lesser already has one. However, their degrees are in different subjects. Name both of them!
Ms. Lesser - Genetics
Mr. Chatterjee - Teaching Social Studies
For what solutions of x make the equation 12x - 24 = 4(3x - 6) valid?
There are infinite solutions.
Write a single inequality to represent this situation: "A truck must be less than 13 feet tall to fit under a bridge, but it must be at least 8 feet tall to carry its current load."
8 < x < 13
Solve the equation 8x + 4 = 2(4x + 3). What are the possible solutions for x?
This results in 8x + 4 = 8x + 6, or 4 = 6. Since this is not true, there are no solutions to this equation.
A booster club buys pom poms for $0.85 each and sells them for $1.50 each. Write an equation for the profit (p) made after selling n pom poms. How many pom poms would it take for the booster club to sell to achieve $66 in profit?
p = 0.65n
102 pompoms
What is Mr. Chatterjee's favorite number? (Hint: it is positive, nonzero, and less than 1,000)
324