Lesson 2: Practice Problems

Problem 1

Which of the changes would keep the hanger in balance? Select all that apply.

A balanced hanger diagram with a square and triangle on the left and 2 red circles and a square on the right.

Adding two circles on the left and a square on the right
Adding 2 triangles to each side
Adding two circles on the right and a square on the left
Adding a circle on the left and a square on the right
Adding a triangle on the left and a square on the right

Problem 2

Here is a balanced hanger diagram.

A balanced hanger diagram with 4 squares, 2 triangles, 2 circles on the left and 2 squares, 1 triangle, 3 circles on the right

Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and $x$ represents the weight of each square. Select all equations that represent the hanger.

$x + x + x + x + 11 = x + 11.5$
$2 x = 0.5$
$4 x + 5 + 6 = 2 x + 2.5 + 6$
$2 x + 2.5 = 3$
$4 x + 2.5 + 2.5 + 3 + 3 = 2 x + 2.5 + 3 + 3 + 3$

Problem 3

What is the weight of a square if a triangle weighs 4 grams?

Explain your reasoning.

A balanced hanger diagram with a triangle and 2 squares on the left and 3 triangles and square on the right

Problem 4 From Unit 4 Lesson 1

Andre came up with the following puzzle. “I am three years younger than my brother, and I am 2 years older than my sister. My mom’s age is one less than three times my brother’s age. When you add all our ages, you get 87. What are our ages?”

Try to solve the puzzle.
Jada writes this equation for the sum of the ages: $(x) + (x + 3) + (x - 2) + 3 (x + 3) - 1 = 87$ . Explain the meaning of the variable and each term of the equation.
Write the equation with fewer terms.
Solve the puzzle if you haven’t already.

Problem 5 From Unit 3 Lesson 8

These two lines are parallel. Write an equation for each.

Two parallel lines on a coordinate grid. The first one crosses the y axis at (0,0) and the second one at (0,3.2)