Question

1. for each diagram, decide if y is an increase or a decrease relative to x. then determine the percent increase or decrease.

a
x

y
b
x

y

1. draw diagrams to represent the following situations.

a. the amount of flour that the bakery used this month was a 40% increase relative to last month.
b. the amount of milk that the bakery used this month was a 75% decrease relative to last month.

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

a. 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.

Explanation:

Problem 1: Diagram Analysis (A and B)

Part A

Step1: Analyze length of x and y

x has 4 units, y has 3 units. So y < x, decrease.

Step2: Calculate percent decrease

Percent decrease = $\frac{x - y}{x} \times 100\% = \frac{4 - 3}{4} \times 100\% = 25\%$

Step1: Analyze length of x and y

x has 4 units, y has 5 units. So y > x, increase.

Step2: Calculate percent increase

Percent increase = $\frac{y - x}{x} \times 100\% = \frac{5 - 4}{4} \times 100\% = 25\%$

• Let last month's flour be 100% (represented by a bar of length, say, 10 units).
• This month's flour is 100% + 40% = 140% of last month. So draw a bar 1.4 times the length of last month's bar. Label last month as "x" (10 units) and this month as "y" (14 units), with a note "40% increase from x to y".

Part b: 75% Decrease in Milk

Answer:

Decrease, 25% decrease

Part B