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09 Jun 2022, 00:45
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (02:26) correct
27%
(02:45)
wrong
based on 118
sessions
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A furniture company makes two types of desks: type \(A\), and type \(B\). If in a certain year \(\frac{3}{8}\) of the desks were of type \(B\), and the production cost of a type \(B\) desk was \(\frac{8}{3}\) that of a type \(A\) desk, then the total cost of producing type \(A\) desks was what fraction of the total cost of producing desks that year?
a) \(\frac{5}{11}\)
b) \(\frac{11}{24}\)
c) \(\frac{13}{24}\)
d) \(\frac{11}{13}\)
e) \(\frac{5}{13}\)
a) \(\frac{5}{11}\)
b) \(\frac{11}{24}\)
c) \(\frac{13}{24}\)
d) \(\frac{11}{13}\)
e) \(\frac{5}{13}\)
Updated on: 09 Jun 2022, 05:26
Originally posted by EthanTheTutor on 09 Jun 2022, 00:56.
Last edited by EthanTheTutor on 09 Jun 2022, 05:26, edited 1 time in total.
Last edited by EthanTheTutor on 09 Jun 2022, 05:26, edited 1 time in total.
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EthanTheTutor
Method 1 - Choosing values:
Since this question involves only fractions, with no specific values, we are free to choose values.
"If in a certain year \(\frac{3}{8}\) of the desks were of type \(B\)"
⇒ Choose \(A=5\) and \(B=3\)
"the production cost of a type \(B\) desk was \(\frac{8}{3}\) that of a type \(A\) desk"
⇒ Choose \(C_A=3\) and \(C_B=8\)
Total Cost of \(A = A\cdot C_A = 3\cdot5\)
Total Cost of \(B = B\cdot C_B = 8\cdot3\)
"the total cost of producing type \(A\) desks was what fraction of the total cost of producing desks that year?"
⇒ \(\frac{{Total Cost A}}{{Total Cost A + Total Cost B}}=\frac{{3\cdot5}}{{3\cdot5+8\cdot3}}=\frac{5}{13}\)
Answer E.
09 Jun 2022, 02:56
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Let the total number of desks be x and the production cost of one type A desk be y.
Then the number of type B desk will be 3/8x and of type A desk will be x-3/8x = 5/8x.
Also, the production cost of one type B desk will be 8/3y.
Now, the total production of A will be 5/8xy
The total production cost will be 5/8x*y + 3/8x*8/3y = 13/8xy
So, ratio of production cost of A to total cost = (5/8xy)/(13/8xy) = 5/13
Thus, the correct option is E.
Then the number of type B desk will be 3/8x and of type A desk will be x-3/8x = 5/8x.
Also, the production cost of one type B desk will be 8/3y.
Now, the total production of A will be 5/8xy
The total production cost will be 5/8x*y + 3/8x*8/3y = 13/8xy
So, ratio of production cost of A to total cost = (5/8xy)/(13/8xy) = 5/13
Thus, the correct option is E.
