A machinist must follow a part drawing with scale 1 to 24. Find the dimensions of the finished stock shown in the illustration. That is, find lengths A, B, C, D.
A) A = 74 in., B = 11 in., C = 54 in., D = 5 in.
B) A = 10 in., B = 74 in., C = 52 in., D = 5 in.
C) A = 74 in., B = 10 in., C = 52 in., D = 4 in.
D) A = 4 in., B = 52 in., C = 10 in., D = 74 in.
E) A = 74 in., B = 10 in., C = 4 in., D = 52 in.

Question

A machinist must follow a part drawing with scale 1 to 24. Find the dimensions of the finished stock shown in the illustration. That is, find lengths A, B, C, D. 
A) A = 74 in., B = 11 in., C = 54 in., D = 5 in. 
B) A = 10 in., B = 74 in., C = 52 in., D = 5 in. 
C) A = 74 in., B = 10 in., C = 52 in., D = 4 in. 
D) A = 4 in., B = 52 in., C = 10 in., D = 74 in. 
E) A = 74 in., B = 10 in., C = 4 in., D = 52 in.

Quizplus · Accepted Answer

Using the scale 1 to 24, we can write the following equations:
A/24 = 74/x
B/24 = 10/x
C/24 = 52/x
D/24 = 4/x
Solving for x in each equation to find the actual dimension:
x = (74*24)/A
x = (10*24)/B
x = (52*24)/C
x = (4*24)/D
Substituting the values of A, B, C, and D in each equation and solving, we get:
x = 192
x = 288
x = 138.46
x = 144
Therefore, the correct dimensions are:
A = 74*24/192 = 9.25*24 = 222 inches
B = 10*24/288 = 0.83*24 = 20 inches
C = 52*24/138.46 = 9.03*24 = 217 inches(rounded to the nearest inch)
D = 4*24/144 = 0.67*24 = 16 inches
Therefore, the answer is C, A = 74 in., B = 10 in., C = 52 in., D = 4 in.

A Machinist Must Follow a Part Drawing with Scale 1