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10 May 2017, 02:19
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
70% (02:29) correct
30%
(02:41)
wrong
based on 303
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A collection of quality cigars went on sale, 3/7 of which were sold at $20.50 each while 1/4 were sold at $35 each. If the total revenue was $491, how many cigars were left unsold?
A. 9
B. 11
C. 14
D. 19
E. 28
A. 9
B. 11
C. 14
D. 19
E. 28
10 May 2017, 06:31
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Bunuel
Nice question!
We can actually solve it WITHOUT using the information about total revenue being $491
Let x = TOTAL number of cigars.
3/7 sold at $20.50 each and 1/4 were sold at $35 each
So, (3/7)x sold for $20.50 each, and (1/4)x sold for $35 each
Total # of cigars SOLD = (3/7)x + (1/4)x
= 3x/7 + x/4
= 12x/28 + 7x/28
= 19x/28
= (19/28)x
So, we can see that 19/28 of the x cigars were sold
This means that 9/28 of the x cigars were NOT sold
In other words, the # of cigars left UNSOLD = 9x/28
Since we know that the # of cigars must be an INTEGER, we can conclude that x is divisible by 28
Also, since we can write 9x/28 as 9(x/28), we can see that the # of cigars left UNSOLD must be a multiple of 9
Check the answer choices...only 1 is a multiple of 9
Answer:
Cheers,
Brent
General Discussion
10 May 2017, 06:39
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Bunuel
Now let's solve the question by using the information about total revenue being $491
Let x = TOTAL number of cigars.
3/7 sold at $20.50 each...
So, (3/7)x = # of cigars sold for $20.50 each
So, (3/7)(x)($20.50) = total sales from $20.50-cigars
...and 1/4 were sold at $35 each
So, (1/4)x = # of cigars sold for $35 each
So, (1/4)(x)($35) = total sales from $35-cigars
The total revenue was $491
So, (3/7)(x)($20.50) + (1/4)(x)($35) = $491
To eliminate the fractions, multiply both sides by 28 to get: (12)(x)(20.50) + (7)(x)(35) = (491)(28)
Simplify: 246x + 245x = (491)(28)
Simplify: 491x = (491)(28)
Divide both sides by 491 to get: x = 28
So, we STARTED with 28 cigars.
3/7 of 28 = 12, so 12 cigars were sold for $20.50 each
1/4 of 28 = 7, so 7 cigars were sold for $35 each
So, total cigars SOLD = 12 + 7 = 19
So, the # of cigars left UNSOLD = 28 - 19 = 9
Answer:
Cheers,
Brent
