SOLUTION: Hi
Rex had altogether 212 $1 & $5 notes. After using 1/3 of the $1 notes,he took out another 12 $5 notes from his cash box. Now the number of 5 dollar notes he has is 1/4 the numb
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Rex had altogether 212 $1 & $5 notes. After using 1/3 of the $1 notes,he took out another 12 $5 notes from his cash box. Now the number of 5 dollar notes he has is 1/4 the numb
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Question 1174647: Hi
Rex had altogether 212 $1 & $5 notes. After using 1/3 of the $1 notes,he took out another 12 $5 notes from his cash box. Now the number of 5 dollar notes he has is 1/4 the number of 1 dollar notes remaining.
How many 5 dollar notes did he have at first.
Thanks
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Your Answer:
Rex had altogether 212 $1 & $5 notes.
let a = no. of $1 notes
let b = no. of $5 notes
therefore
a + b = 212
or
a = (212-b), use this form for substitution
:
After using 1/3 of the $1 notes, he took out another 12 $5 notes from his cash box.
Now a = $1 notes remain in the cash box
and
(b-12) = $5 notes remain in the cash box
:
Now the number of 5 dollar notes he has is 1/4 the number of 1 dollar notes remaining.
b - 12 = *a
b - 12 = a
reduce fraction
b - 12 = a
multiply both sides by 6
6(b-12) = a
6b - 72 = a
replace a with (212-b)
6b - 72 = 212 - b
6b + b = 212 + 72
7b = 284
b = 284/7
b = 40.157
These kind of problems have to have integer solutions, something is wrong with this problem!!
:
How many 5 dollar notes did he have at first.
As one tutor says, the wording of the problem makes the information unclear.
Interpreted one way, as the other tutor did, the problem comes out with a nonsensical answer, with the numbers of each kind of bill not being whole numbers.
The way I read the problem the first time, the problem does have a solution.
The phrase that causes the problem is "... he took another 12 $5 notes from his cash box".
The other tutor interpreted that as decreasing the number of $5 bills by 12; that is a reasonable interpretation.
The first time I read the problem, I interpreted it to mean he went to his cash box and got 12 MORE $5 bills to add to what he already had. Also a reasonable interpretation.
The fact that the wording allows two very different reasonable interpretations means the statement of the problem is defective.
--------------------------------------
Assuming my interpretation....
x = original number of $1 notes
212-x = original number of $5 notes
(2/3)x = number of $1 notes after he used 1/3 of the original number
(212-x)+12 = number of $5 notes after he added 12 more from his cash box
The number of $5 notes was now 1/4 the number of $1 notes.
The original number of $1 notes was 192; the original number of $5 notes was 212-192 = 20.
