Question

esson practice 10 name: emily phong date: 9/9 period: problems 1–4: ali and kiana buried treasure together on their school’s field. the field is 00 feet wide. ali made a map that is 8 inches wide to record its location. . write two possible scales ali could have used to make this map. . kiana made her own map using a scale of 1 inch to 20 feet. whose map is larger: kiana’s or ali’s? explain your thinking.

Explanation:

Part 1: Writing two possible scales for Ali's map

First, we know the actual width of the field (let's assume the missing number before "00 feet" is 100, as it's a common field width; if it's a different number, the process is similar). Let's take the actual width as 100 feet (1200 inches, since 1 foot = 12 inches) and the map width as 8 inches.

Scale 1: Simplify the ratio of map inches to actual inches

Step 1: Convert actual width to inches

Actual width = 100 feet = \( 100 \times 12 = 1200 \) inches.
Map width = 8 inches.

Step 2: Find the scale ratio

Simplify \( \frac{8}{1200} = \frac{1}{150} \).
So one scale is \( 1 \) inch : \( 150 \) inches (or \( 1 \) inch : \( 12.5 \) feet, since \( 150 \div 12 = 12.5 \)).

Scale 2: Use a simpler ratio (e.g., 1 inch to a round number of feet)

Let’s choose a scale where 8 inches on the map represents 80 feet (a round number).

Step 1: Define the ratio

Map width = 8 inches, Actual width = 80 feet.

Step 2: Simplify the ratio

Divide both by 8: \( \frac{8}{8} \) inch : \( \frac{80}{8} \) feet \( = 1 \) inch : \( 10 \) feet.

Part 2: Comparing Ali’s (using the first scale: 1 inch : 12.5 feet) and Kiana’s (1 inch : 20 feet) maps

Step 1: Calculate map width for Kiana

Actual width = 100 feet.
Kiana’s scale: 1 inch = 20 feet.
Map width for Kiana = \( \frac{100}{20} = 5 \) inches.

Step 2: Compare map widths

Ali’s map width = 8 inches (given).
Kiana’s map width = 5 inches.
Since \( 8 > 5 \), Ali’s map is larger.

Final Answers

1. Two possible scales: \( \boldsymbol{1} \) inch : \( \boldsymbol{12.5} \) feet and \( \boldsymbol{1} \) inch : \( \boldsymbol{10} \) feet (or other valid scales).
2. Ali’s map is larger because, for the same actual field width, Ali’s map (8 inches wide) is wider than Kiana’s map (5 inches wide) when calculated using their respective scales.

Answer:

Part 1: Writing two possible scales for Ali's map

First, we know the actual width of the field (let's assume the missing number before "00 feet" is 100, as it's a common field width; if it's a different number, the process is similar). Let's take the actual width as 100 feet (1200 inches, since 1 foot = 12 inches) and the map width as 8 inches.

Scale 1: Simplify the ratio of map inches to actual inches

Step 1: Convert actual width to inches

Actual width = 100 feet = \( 100 \times 12 = 1200 \) inches.
Map width = 8 inches.

Step 2: Find the scale ratio

Simplify \( \frac{8}{1200} = \frac{1}{150} \).
So one scale is \( 1 \) inch : \( 150 \) inches (or \( 1 \) inch : \( 12.5 \) feet, since \( 150 \div 12 = 12.5 \)).

Scale 2: Use a simpler ratio (e.g., 1 inch to a round number of feet)

Let’s choose a scale where 8 inches on the map represents 80 feet (a round number).

Step 1: Define the ratio

Map width = 8 inches, Actual width = 80 feet.

Step 2: Simplify the ratio

Divide both by 8: \( \frac{8}{8} \) inch : \( \frac{80}{8} \) feet \( = 1 \) inch : \( 10 \) feet.

Part 2: Comparing Ali’s (using the first scale: 1 inch : 12.5 feet) and Kiana’s (1 inch : 20 feet) maps

Step 1: Calculate map width for Kiana

Actual width = 100 feet.
Kiana’s scale: 1 inch = 20 feet.
Map width for Kiana = \( \frac{100}{20} = 5 \) inches.

Step 2: Compare map widths

Ali’s map width = 8 inches (given).
Kiana’s map width = 5 inches.
Since \( 8 > 5 \), Ali’s map is larger.

Final Answers

1. Two possible scales: \( \boldsymbol{1} \) inch : \( \boldsymbol{12.5} \) feet and \( \boldsymbol{1} \) inch : \( \boldsymbol{10} \) feet (or other valid scales).
2. Ali’s map is larger because, for the same actual field width, Ali’s map (8 inches wide) is wider than Kiana’s map (5 inches wide) when calculated using their respective scales.