snipertrader wrote:
30.Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by
Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many
hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of
hours it took to produce the deluxe stereos last month was what fraction of the total
number of hours it took to produce all the stereos?
A.7/17
B.14/31
C. 7/15
D.17/35
E.1/2
Solution
2/3 were basic so 1/3 will be deluxe
Assuming it took 1 hr to complete Basic stereo ; deluxe will take 7/5 X 1 hr
Total time taken (basic radio + deluxe radio) = 2/3 + (1/3 x 7/5) = 17/15
Ratio of hrs needed for deluxe ratio to total hrs = (7/15)/(17/15) = 7/17
I can't seem to figure out why you multiplied 1/3 by 7/5. I assume you are right because the answer I get isn't one of the choices, so I'm hoping someone can explain to me why this was done. I try to solve these problems using a small chart: (Total=Rate*Time)
As you stated, let's assume it takes 1 hr to make a B stereo.
Basic Total = 2/3
Rate = x
time = 1hr
therefore rate (x) = (2/3) / 1 = 2/3 DeluxeTotal = 1/3
Rate = y
time = 7/5 *1hr = 7/5
therefore rate (y) = (1/3) / (7/5) = 5/21so 1/x + 1/y = 1/total time (t)
1/(2/3) + 1/(5/21) = 1/t
t = 3/2 + 21/5 = 15/10 + 42/10 =
57/10so to find the fraction of Deluxe Time/Total time = (7/5)/(57/10) = not the right answer
I can see that in order to match the snipertrader's solution, I need to rearrange my 'total', 'rate' & 'time' to be:
BasicTotal = x
rate = 1
time = 2/3
Deluxetotal = y
rate = 7/5
time = 1/3
in which case you would get 7/17 as the answer, but I can't make the leap as to why 2/3 and 1/3 need to be the TIME and not the TOTAL? I'm hoping someone can walk me through this.
Thank you!!