Math  /  Algebra

QuestionPierce works at a tutoring center on the weekends. At the center, they have a large calculator to use for demonstration purposes that is a scale model of calculators available for the students to use.
Each key on the student calculators is 18 millimeters wide, and each key on the demonstration calculator is 3.6 centimeters wide. If the student calculators are 255 millimeters tall, how tall is the demonstration calculator? A. 0.036 meter B. 51 meters C. 0.51 meter D. 9.18 meters Reset Next

Studdy Solution

STEP 1

1. Each key on the student calculators is 18 millimeters wide.
2. Each key on the demonstration calculator is 3.6 centimeters wide.
3. The student calculators are 255 millimeters tall.
4. We need to find the height of the demonstration calculator.

STEP 2

1. Convert all measurements to the same unit.
2. Determine the scale factor between the student calculator and the demonstration calculator.
3. Use the scale factor to find the height of the demonstration calculator.

STEP 3

Convert all measurements to the same unit. Since the student calculator's height is given in millimeters, convert the demonstration calculator's key width from centimeters to millimeters.
3.6 cm=36 mm 3.6 \text{ cm} = 36 \text{ mm}

STEP 4

Determine the scale factor between the student calculator and the demonstration calculator by comparing the width of their keys.
Scale factor =Width of demonstration calculator keyWidth of student calculator key = \frac{\text{Width of demonstration calculator key}}{\text{Width of student calculator key}}
=36 mm18 mm=2 = \frac{36 \text{ mm}}{18 \text{ mm}} = 2

STEP 5

Use the scale factor to find the height of the demonstration calculator.
Height of demonstration calculator =Height of student calculator×Scale factor = \text{Height of student calculator} \times \text{Scale factor}
=255 mm×2=510 mm = 255 \text{ mm} \times 2 = 510 \text{ mm}
Convert the height from millimeters to meters:
510 mm=0.51 meters 510 \text{ mm} = 0.51 \text{ meters}
The height of the demonstration calculator is:
0.51 meters \boxed{0.51 \text{ meters}}

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