Question

pierre 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. 9.18 meters b. 0.51 meter c. 51 meters d. 0.035 meter

Explanation:

Step1: Find the scale factor

First, convert the widths to the same unit. The student calculator key width is 18 millimeters, and the demonstration calculator key width is 3.6 centimeters. Convert 3.6 centimeters to millimeters: \(3.6 \text{ cm} = 3.6\times10 = 36 \text{ mm}\). The scale factor \(k\) is the ratio of the demonstration key width to the student key width: \(k=\frac{36}{18}=2\). Wait, no, wait. Wait, maybe I misread. Wait, the problem says "each key on the student calculators is 18 millimeters wide, and each key on the demonstration calculator is 3.6 centimeters wide". Wait, no, maybe the height? Wait, the student calculator is 255 millimeters tall. Wait, let's re - read.

Wait, the problem: "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?"

So first, find the scale factor. Convert 3.6 centimeters to millimeters: \(3.6\space\text{cm}=3.6\times10 = 36\space\text{mm}\). The scale factor \(k\) (demonstration to student) for key width is \(\frac{36}{18}=2\)? Wait, no, that can't be. Wait, maybe I messed up. Wait, 3.6 centimeters is 36 millimeters, and student key is 18 millimeters. So the scale factor is \(36\div18 = 2\)? But then the height of the demonstration calculator would be \(255\times2=510\) millimeters, which is 0.51 meters? Wait, 510 millimeters is 0.51 meters? Wait, 1 meter = 1000 millimeters, so 510 millimeters=\(\frac{510}{1000}=0.51\) meters? Wait, no, 510 millimeters is 0.51 meters? Wait, 510 divided by 1000 is 0.51? Wait, 510 millimeters = 0.51 meters? Wait, 1 meter = 1000 millimeters, so 255 millimeters is 0.255 meters. Wait, maybe the scale factor is based on the key width. Let's do it properly.

Step 1: Convert the key width of the demonstration calculator to millimeters. Since 1 cm = 10 mm, \(3.6\space\text{cm}=3.6\times10 = 36\space\text{mm}\).

Step 2: Find the scale factor. The scale factor \(s\) is the ratio of the demonstration key width to the student key width. So \(s=\frac{36\space\text{mm}}{18\space\text{mm}} = 2\). Wait, that seems too small. Wait, no, maybe I have the ratio reversed. Wait, maybe the student key is 18 mm, demonstration key is 3.6 cm = 36 mm. So the demonstration is larger. So the scale factor from student to demonstration is \(36\div18 = 2\). Then, the height of the demonstration calculator is the height of the student calculator times the scale factor. The student calculator is 255 mm tall. So demonstration height \(h = 255\space\text{mm}\times2=510\space\text{mm}\).

Step 3: Convert 510 millimeters to meters. Since 1 meter = 1000 millimeters, \(h=\frac{510}{1000}=0.51\space\text{meters}\).

Answer:

B. 0.51 meter