3.7.1: Preparation 3.7

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(1) Ben has $75 in his savings account. He plans to deposit $35 per week to build his account balance.

(a) Complete the following equation to represent the amount of money (A) Ben will have in his account after any number of weeks. Use x as your input variable.

A =

(b) What does the input variable (x) represent in this problem?

(c) Which of the following values could be the value of the input variable (x) in this context? There may be more than one correct answer.

(i) -5

(ii) 3

(iii) 4.2

(iv) 18

(d) Ben wants to use his savings to buy a computer for $740. Use the equation from part (a) to determine the number of weeks it will take him to save enough money to buy the computer.

Proportionality

Length-to-width and width-to-length ratios

The dimensions of a figure can be written as a ratio. Imagine a rectangle with a length of ten inches and a width of three inches.

Diagram showing a rectangle, indicating the following:
Width = 3 inches
Length = 10 inches

You can say that the ratio of the length to width is 10:3 or 10/3. It is also correct to say that the ratio of the width to length is 3:10 or 3/10.

In Collaboration 3.7, when we compare multiple figures using their respective ratios, it will be important to be consistent.

Equivalent Fractions (review)

As you recall from Unit 3.1, equivalent fractions (ratios) can be written in many equivalent forms. For example, all of the following fractions simplify to 10/3 in lowest terms: 10/3 = 20/6 = 30/9 = 100/30

Proportional Figures

Now, we can define what it means for two figures to be proportional. Consider the following figures and compare them using their length-to-width ratios.

Small rectangle:
Width = 3 inches
Length = 10 inches Large rectangle:
Width = 6 inches
Length = 20 inches

The length-to-width ratio of the figure on the left is 10/3.

The length-to-width ratio of the figure on the right is 20/6 = 10/3 in lowest terms. Note that 10/3 and 20/6 are equivalent fractions.

While these figures are not equivalent, they are proportional to each other because their dimensions have the same ratio.

(2) Use the figure below to answer the following questions.

Diagram showing the cylinder, indicating the following:
Height = 9 feet
Width = 5 feet

(a) Write the ratio of the dimensions of the cylinder shown above in the form of diameter to height.

(b) Give the dimensions of a cylinder that would be proportional to the one shown.

Diameter:

Height:

(3) Which of the following fractions has a ratio of 4:3? There may be more than one correct answer.

(i) $\dfrac{24}{18}$

(ii) $\dfrac{16}{9}$

(iii) $\dfrac{9}{12}$

(iv) $\dfrac{20}{15}$

(v) $\dfrac{8.8}{6.6}$

After Preparation 3.7 (survey)

You should be able to do the following things for the next collaboration. Rate how confident you are on a scale of 1–5 (1 = not confident and 5 = very confident).

Before beginning Collaboration 3.7, you should understand the concepts and demonstrate the skills listed below.

Skill or Concept: I can …	Rating from 1 to 5
interpret the meaning of ratios, including when written as fractions.
understand the use of a variable to represent an unknown.
solve a two-step equation such as 2x + 9 = 13.

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