Lesson 6

Increasing and Decreasing

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Problem 1

For each diagram, decide if \(y\) is an increase or a decrease relative to \(x\). Then determine the percent increase or decrease.

Tape diagrams A and B.

Solution

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Problem 2

Draw diagrams to represent the following situations. 

  1. The amount of flour that the bakery used this month was a 50% increase relative to last month.
  2. The amount of milk that the bakery used this month was a 75% decrease relative to last month.

Solution

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Problem 3

Write each percent increase or decrease as a percentage of the initial amount. The first one is done for you.

  1. This year, there was 40% more snow than last year.

    The amount of snow this year is 140% of the amount of snow last year.

  2. This year, there were 25% fewer sunny days than last year.
  3. Compared to last month, there was a 50% increase in the number of houses sold this month.
  4. The runner’s time to complete the marathon was a 10% less than the time to complete the last marathon.

Solution

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Problem 4

The graph shows the relationship between the diameter and the circumference of a circle with the point \((1,\pi)\) shown. Find 3 more points that are on the line.

A graph of a line in the coordinate plane with the origin labeled O.

Solution

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(From Unit 3, Lesson 3.)

Problem 5

Priya bought \(x\) grams of flour. Clare bought \(\frac38\) more than that. Select all equations that represent the relationship between the amount of flour that Priya bought, \(x\), and the amount of flour that Clare bought, \(y\).

A:

\(y=\frac38 x\)

B:

\(y=\frac58 x\)

C:

\(y=x+\frac38x\)

D:

\(y=x -\frac38 x\)

E:

\(y=\frac{11}{8}x\)

Solution

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(From Unit 4, Lesson 4.)