Need Help With ASVAB Practice Question

[Kam98]

So I need help understanding the answer to this question, the app I’m using shows me an explanation but I’m not really understanding it because it’s so vague. Would someone mind explaining how to get the answer to this question for me?

 

[Deleted member 4993]

So I need help understanding the answer to this question, the app I’m using shows me an explanation but I’m not really understanding it because it’s so vague. Would someone mind explaining how to get the answer to this question for me?

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Please share your work/thoughts about this assignment.

 

[HallsofIvy]

The problem asks for "the number of cooks required" so I would start "Let "c" be the number of cooks. Further each cook can bake cakes or cookies so I would let c1 be the number of cooks baking large cakes and c2 the number of cooks baking small cakes. Either number can be fractional if one or more cooks bakes both cookies and cakes. Of course, c= c1+ c2. Since "each cook can bake 5 large cakes per hour" the c1 cooks bake 5c1 cakes per hour and in 3 hours will bake 15c1 large cakes. We must have 29 large cakes so we want 15c1= 29. Since "each cook can bake 14 small cakes small cakes per hour" c2 cooks can bake 14c2 small cakes per hour and 42c2 small cakes in 3 hours. We must have 260 small cakes so we want 42c2= 260.

Then c1= 29/15= 1 and 14/15 and c2= 260/42= 130/21= 6 and 4/21 so c= 1+ 14/15+ 6+ 4/21= 7+ 98/105+ 20/105= 7+ 118/105. Since c, the number of cooks, must be an integer, we will need 8 cooks, though one or more cooks must be idle part of the time.

 

[Dr.Peterson]

Then c1= 29/15= 1 and 14/15 and c2= 260/42= 130/21= 6 and 4/21 so c= 1+ 14/15+ 6+ 4/21= 7+ 98/105+ 20/105= 7+ 118/105. Since c, the number of cooks, must be an integer, we will need 8 cooks, though one or more cooks must be idle part of the time.

But 7+118/105 = 8+13/105, so we need at least 9 cooks. I'd say 2 are working on large cakes and 7 on small cakes, rounding each number up individually.

My approach was that the large cakes require 29/5 = 5.8 cook-hours (29 cakes at 1/5 cook-hour per cake), which means 2 cooks for 3 hours, and small cakes need 260/14 = 18.6 cook-hours (260 cakes at 1/14 cook-hour per cake), or 7 cooks for 3 hours, since 6 would be too few.

 

[JeffM]

The problem is not well written. It does not say whether a cook can work on both small and large cakes during the same hour.

If not, two cooks can bake 29 large cakes in three hours (2 * 5 * 3) = 30 > 29
whereas one cook can only bake (1 * 5 * 3) = 15 < 29, and
seven cooks can bake (7 * 14 * 3) = 294 > 260
whereas six cooks can bake (6 * 14 * 3) = 252 < 260. But if we have 7 cooks working on small cakes, one makes only 8 cakes, which leaves two hours for that cook to bake 10 large cakes. But 15 + 10 < 29 so 2 + 7 = 9 cooks are needed.

The problem is slightly more complex if a cook can work on more than one type of cake during the same hour. The cook who bakes only four large cakes during an hour will have one-fifth of an hour available to work on small cakes. Presumably that means that cook has time to bake 2 small cakes, but 252 + 2 = 254 < 260. The cook who bakes only 8 small cakes in 3 hours has 2 + 6\14ths of an hour to bake large cakes, which translates at 5 cakes per hour into fewer than 13 cakes, and 15 + 12 = 27 < 29. So, we still need 9 cooks.

 

[Steven G]

I agree with JeffM that the problem is not well written. It does not say whether a cook can work on both small and large cakes during the same hour.

 

[Deleted member 4993]

I agree with JeffM that the problem is not well written. It does not say whether a cook can work on both small and large cakes during the same hour.

Too many cooks spoil the cake!!!