SOLUTION: A donut shop sold 3/5 of their glazed donuts in the morning, In the afternoon, they sold 5/6 of the remaining glazed donuts. The ratio of the remaining glazed donuts to the remaini

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A donut shop sold 3/5 of their glazed donuts in the morning, In the afternoon, they sold 5/6 of the remaining glazed donuts. The ratio of the remaining glazed donuts to the remaini      Log On


   

Question 1210595: A donut shop sold 3/5 of their glazed donuts in the morning, In the afternoon, they sold 5/6 of the remaining glazed donuts. The ratio of the remaining glazed donuts to the remaining chocolate donuts was 2:7. If they had 42 chocolate donuts left, how many total donuts (glazed + chocolate) did the shop have at the very beginning?
Found 2 solutions by KMST, ikleyn:
Answer by KMST(5345) About Me  (Show Source):
You can put this solution on YOUR website!
Not enough information.
We know how many chocolate donuts the donut shop had at the end of the day,
and could calculate how many glazed donut the donut shop had at the end of the day,
but without more information there is no way to calculate how many chocolate donuts the donut shop had at the very beginning.

Answer by ikleyn(53750) About Me  (Show Source):
You can put this solution on YOUR website!
.
A donut shop sold 3/5 of their glazed donuts in the morning.
In the afternoon, they sold 5/6 of the remaining glazed donuts.
The ratio of the remaining glazed donuts to the remaining chocolate donuts was 2:7.
If they had 42 chocolate donuts left, how many total donuts (glazed + chocolate) did the shop have
at the very beginning?
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Let 'x' be the number of glazed donuts in the chop at the very beginning.
Let 'c' be the number of remaining chocolate donuts, which number is mentioned in the problem:  c = 42.


In the morning the shop sold  %283%2F5%29x  of their glazed donuts.
Hence,  %282%2F5%29x  glazed donuts remained.


Of this  %282%2F5%29x  glazed donuts,  5%2F6  were sold afternoon.
So,  %282%2F5%29x%2A%285%2F6%29 = %281%2F3%29x  glazed donuts were sold afternoon.

Thus  %283%2F5%29x + %281%2F3%29x = %289%2F15%29x+%2B+%285%2F15%29x = %2814%2F15%29x  glazed donuts 
were sold during the day, and  %281%2F15%29x  glazed donut remained at the evening.


From the condition, we can write

    %28%281%2F15%29x%29%2Fc = 2%2F7,  or  x%2F%2815c%29 = 2%2F7,

which gives 

    x = %28%282%2A15%29%2F7%29c.

Substitute here c= 42 to get  

    x = %28%282%2A15%29%2F7%29%2A42 = 2*15*6 = 180.


So, the starting number of the glazed donuts was 180 at the very beginning.


It is what we can get from the given problem, using all given information.


But we have no any other data to determine the number of the chocolate donuts at the very beginning.


So, in the given form, the problem is DEFECTIVE and does not allow to answer the posed question.

Analyzed as far as it is possible with explanation WHY the problem is FAULT.