Q: Suppose a construction company uses 6 teams to build a house in 80 days. If they want to finish the house in just 16 days, how many teams must they employ? Assume the relationship is inversely proportional.

$$\dfrac{6 \times 80}{16} = 30$$ teams

Question 1

Suppose a construction company uses 6 teams to build a house in 80 days. If they want to finish the house in just 16 days, how many teams must they employ? Assume the relationship is inversely proportional.

Accepted Answer

$$\dfrac{6 	imes 80}{16} = 30$$ teams

Question 2

Which equation best represents the relationship between the number of teams $$t$$ and the number of days $$d$$ needed to build the house, if the relationship is inversely proportional?

Accepted Answer

$$t 	imes d = k$$

Question 3

What does it mean to solve an equation involving variables?

Accepted Answer

To determine the values for the variables that make the equation true.

Question 4

Given the equation $$5 + 3 = ? + 2$$, what value of $$?$$ will make the pans balance?

Accepted Answer

$$6$$

Question 5

Which of the following is an example of an identity?

Accepted Answer

$$A(B + C) = AB + AC$$

Question 6

If $$A = L 	imes W is $$used to find the area of a rectangle, what type of equation is this?

Accepted Answer

A formula relating two or more quantities

Question 7

A strip diagram shows Markus had some money. He spent $$\dfrac{1}{4} of it$$, then gave $$\dfrac{1}{2} of $$what was left to Lila. If he started with $$x$$ dollars, how much did he give to Lila?

Accepted Answer

$$\dfrac{1}{2}(x - \dfrac{1}{4}x)$$

Question 8

Which of the following best describes the use of a strip diagram in solving algebra word problems?

Accepted Answer

It provides a visual representation of quantities and their relationships.

Question 9

If $$8 + 7 = 15$$, what type of equation is this?

Accepted Answer

A calculation result

Question 10

A company needs to transport 13 kilograms of material using containers that each hold $$x$$ kilograms. Which equation represents the number of containers $$n$$ needed?

Accepted Answer

$$n = \dfrac{13}{x}$$

Question 11

Which of the following is NOT a tip for using strip diagrams effectively?

Accepted Answer

Always make strips exactly proportional to the quantities.

Question 12

If $$t$$ teams can build a house in $$d$$ days, and the relationship is inversely proportional, what happens to $$d if$$ $$t is $$doubled?

Accepted Answer

$$d is $$halved

Question 13

Which equation would you solve to find the number of liters $$x if$$ $$250$$ dollars buys $$x$$ liters at $$13$$ dollars per liter?

Accepted Answer

$$13x = 250$$

Question 14

Which of the following equations is an example of the distributive property?

Accepted Answer

$$A(B + C) = AB + AC$$

Question 15

If $$5 + 3 = x + 2$$, what is the value of $$x$$?

Accepted Answer

$$6$$

Equations, Proportional Reasoning, and Visual Models in Algebra

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