The first question on the 08/09 Study List is giving me fits.
"Mary uses a faulty ruler to measure a distance. She measured 45 ft, 4.77in, but corrected her measurement after realizing that the 1 yd ruler was actually 1 yd, .11in. What is the % difference between the corrected length Mary measured and Yolanda's independent measurement of 45 ft, 5.36in?"
Step 1: Convert everything to inches
Mary's Measurement: 12*45 + 4.77 = 544.77 in
What Mary thought the length of the ruler was: 12*3 = 36 in
The ruler's actual length: 36+.11 = 36.11 in
Yolanda's Measurement: 12*45+5.36 = 545.36 in
Step 2: Figure out Mary's corrected measurement
We know that she thought that she was using a 36 in ruler, but actually she was using a 36.11 in ruler. She calculated the distance to the object using the following formula: Total distance = (36 in)(# of full ruler lengths) + Remaining measurement. But she should have done: Total distance = (36.11 in)(# of ruler lengths) + Remaining measurement. We can set up two equalities:
Original formula: 544.77 in = (36 in)(# of ruler lengths) + Remaining measurement
Corrected formula: Corrected Distance = (36.11 in)(# of ruler lengths) + Remaining measurement
Using elimination we get: (Corrected Distance) = (.11 in)(# of ruler lengths) + 544.77 in
Since the number of ruler lengths and the Remaining measurement must be the same in both equations, we can use the original formula to determine the amount of full lengths of the yard stick used. 544.77 in / 36 in = 15 full lengths and change. Therefore, our # of ruler lengths = 15. Plugging this into our new equation, we obtain:
Corrected Distance = (.11 in)(15) + 544.77 in = 546.42 in
Step 3 : use the % difference formula and solve the answer
The formula for percent difference (already in percent) according to wikipedia given two values x and y is the following:
[200|x-y|]/[x+y]
Letting the Mary's corrected measurement be x, and Yolanda's measurement be y, we get: 200|546.42-545.36|/[546.42+545.36] = 200(1.06)/(1091.78) = .19%
Answer = .19%
This is WRONG!!!!!!!!!!!! AND I DON'T KNOW WHY! Somebody please help me correct this mess!
Zack