David W. answered • 01/11/17
Tutor
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(90)
Experienced Prof
This is a simple inventory problem (much like reconciling your checkbook with bank statements each month -- starting balance, checks/debits, deposits/credits, ending balance):
Starting New
Inventory Sold Buy Back Inventory
A: 36 17 2 21
B: 84 15 69
C: 504 3 501
--------------------------------------------------------------
T: 624 35 2 591
Note that "17/36" is a fraction, but here it is used to indicate "17 of 36." That is, the shopkeeper sold 17 of the 36 items A that he had, bought back 2 and ended with 21 (the new inventory for item A). Next month, for example, he might sell 11/21 of item A.
In summary, the shopkeeper started with 524 of items A,B,and C and ended with 591 items.
David W.
First, in order to get a single value for an answer, you must either:
(1) know how many items were in inventory in each category (as Michael J. wrote in his answer) and assume that the values, for example 17/36, are indeed fractions of the inventory in that category (thus "of" means multiply), or
(2) otherwise be able to combine independent values to calculate a single answer (for example, if there is only one item type or they are sold in sets).
Now, the denominators of the detractors (the various possible answers) are quite suspicious. They happen to be the denominators of the fractions given in the problem.
We observe that 504 is 14*36 and is 6*84, so 504 is a common multiple of the three denominators. So, the problem could be rewritten (replacing values) as:
“A shopkeeper sold 238/504 of item A.90/504 of item B and 3/504 of item C. He buys back 28/504 of item A. What is the total number of items left with the shopkeeper?”
The net number sold is (238+90+3-28)/504 = 303/504 [this assumes that item A is item B is item C]. Thus, first distractor has a possible explanation – the “A”, “B,” and “C” should have been omitted. Remember, this is the net fraction sold.
Now, 331/504 has an immediate explanation – the 28 was added rather than subtracted. Again, this is the sold portion.
And, 329/504 is adding the 28 and the 3 (still the sold portion).
Now, the shopkeeper has left 28/84=168/504 and 15/36=210/504. Just above, we calculated that 303/504 was the amount sold, so 201 is the amount remaining. This certainly not 210, but it is for a person with dyslexia.
(1) know how many items were in inventory in each category (as Michael J. wrote in his answer) and assume that the values, for example 17/36, are indeed fractions of the inventory in that category (thus "of" means multiply), or
(2) otherwise be able to combine independent values to calculate a single answer (for example, if there is only one item type or they are sold in sets).
Now, the denominators of the detractors (the various possible answers) are quite suspicious. They happen to be the denominators of the fractions given in the problem.
We observe that 504 is 14*36 and is 6*84, so 504 is a common multiple of the three denominators. So, the problem could be rewritten (replacing values) as:
“A shopkeeper sold 238/504 of item A.90/504 of item B and 3/504 of item C. He buys back 28/504 of item A. What is the total number of items left with the shopkeeper?”
The net number sold is (238+90+3-28)/504 = 303/504 [this assumes that item A is item B is item C]. Thus, first distractor has a possible explanation – the “A”, “B,” and “C” should have been omitted. Remember, this is the net fraction sold.
Now, 331/504 has an immediate explanation – the 28 was added rather than subtracted. Again, this is the sold portion.
And, 329/504 is adding the 28 and the 3 (still the sold portion).
Now, the shopkeeper has left 28/84=168/504 and 15/36=210/504. Just above, we calculated that 303/504 was the amount sold, so 201 is the amount remaining. This certainly not 210, but it is for a person with dyslexia.
SPECIAL NOTE: I often make typos, so I’m an expert. I also proofread computer books and articles and often find typos, so I’m pretty good at understanding what someone meant rather than exactly what they said. Computers usually interpret instructions exactly rather than determining the intent, so I also have a huge number of hours spent diagnosing that difference.
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01/11/17