1.2 Exercises

Mary Ann Barbato

1.2 Exercises

Work through examples 1.2.1 through 1.2.5 again using variables as follows:

Step 1: Write an equation for each scale using the variables below

t = the weight of one triangle

c = the weight of one circle

s = the weight of one star

q = the weight of one square

For example, if the (balanced) scale has 4 triangles on one side, and a circle, and a square on the other side, then we write 4t = c + q as the equation.

Step 2: Manipulate these equations to answer the questions. Some manipulations include adding/subtracting equations to get a new equation that is more useful and/or solving for a variable in one equation and plugging it into another equation. Try to avoid using fractions. Show and explain every step. That is, justify where each new equation comes from.

Step 3: State your final answer as a complete sentence (for example: 3 triangles will balance the last scale)

Example 1.2.1 Revisited

a) Based on the scale picture, what can you say about the relationship between the weight of a star and the weight of a circle? Explain how you determined your answer.

b) Based on the scale picture what can you say about the relationship between the weight of a star and the weight of a square? Explain how you determined your answer.

scale: 1 star 1 square equal 3 squares

Example 1.2.2 Revisited

Use Figure 1 to answer the questions that follow.

Balance scale with 2 squares on the left side versus a circle on the right. Balance scale with a triangle on the left side versus a square and circle on the right.

a) Which shape weighs the most? Justify your answer.

b) Which scale is holding the most total weight? How do you know?

Example 1.2.3 Revisited

Use the first two scale pictures in the Figure 2 to gather enough information to determine how many squares go in place of the question mark in the third scale picture.

Balance scale with 2 triangles on the left side versus 6 circles on the right.

Balance scale with 3 triangles on the left side versus 9 squares on the right.

Balance scale with a cirecle on the left side versus a question mark on the right.

Example 1.2.4 Revisited

Use the first three scale pictures in Figure 3 to gather information to determine what shapes will balance the scale below. That is, what can we put in place of the question mark that will balance the scale? Try to come up with more than one answer. Explain how you arrived at your answers.

scale 1: 2 triangles 1 square versus 10 circles scale 2: 1 circle 2 squares equal 3 triangles scale 3: 4 triangles equal 3 square scale 4: ? equal 1 triangle 1 circle

Example 1.2.5 Revisited

Use the scale pictures in Figure 4 to gather information to determine how many squares go in place of each of the question marks in parts (a), (b) and (c) below.

scale 1: 1 circle 1 square equal 1 star scale 2: 1 circle equal 1 square 1 triangle scale 3: 2 stars equal 3 triangles