SOLUTION: Lauri and Anže are baking cookies for a village festival. Anže baked 2/3 as many cookies as Lauri. After the morning rush, Anže had 10 fewer cookies left than the number he had

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Lauri and Anže are baking cookies for a village festival. Anže baked 2/3 as many cookies as Lauri. After the morning rush, Anže had 10 fewer cookies left than the number he had       Log On


   

Question 1210615: Lauri and Anže are baking cookies for a village festival. Anže baked 2/3 as many cookies as Lauri. After the morning rush, Anže had 10 fewer cookies left than the number he had originally baked. Lauri had 1/4 as many cookies left as Anže. By the end of the day, the difference between the number of cookies they each had left was 30. How many cookies did Lauri bake at first?
Found 2 solutions by KMST, ikleyn:
Answer by KMST(5361) About Me  (Show Source):
You can put this solution on YOUR website!
x=number of cookies Lauri baked.
%282%2F3%29x=number of cookies Anže baked
If we assume that "after the morning rush" and "by the end of the day" are the same time, and the time when
Anže had 10 fewer cookies left than the number he had originally baked, and
Lauri had 1/4 as many cookies left as Anže,
we have enough data to solve the problem.
At the end, Anže had %282%2F3%29x-10 cookies left,
while Lauri had %281%2F4%29%28%282%2F3%29x-10%29 cookies left.
The difference is:
cookies, and we are told that
%283%2F4%29%28%282%2F3%29x-10%29=30Multiplying both side times 4%2F3 , we get
%282%2F3%29x-10=40-->%282%2F3%29x=50-->x=50%283%2F2%29-->x=highlight%2875%29

Answer by ikleyn(53846) About Me  (Show Source):
You can put this solution on YOUR website!
.
Lauri and Anže are baking cookies for a village festival. Anže baked 2/3 as many cookies as Lauri.
After the morning rush, Anže had 10 fewer cookies left than the number he had originally baked.
Lauri had 1/4 as many cookies left as Anže. By the end of the day, the difference
between the number of cookies they each had left was 30. How many cookies did Lauri bake at first?
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        This problem is good to solve it by the backward method.
        Doing this way, the solution to the problem becomes simpler. 


Let x be the number of cookies Lauri had left at the end of the day.
Then, according to the problem, Anze had left 4x cookies at the end of the day.


Next, according to the problem, 

    4x - x = 30,  or  3x = 30,  which implies  x = 30/3 = 10.


So, at the end of the day, Lauri had 10 cookies left, while Anze had 4*10 = 40 cookies left.


Hence, initially Anze did bake 40 + 10 = 50 cookies.


These 50 cookies are 2/3 of the number of cookies that Lauri initially baked.


Hence, Lauri baked initially  %283%2F2%29%2A50 = 3*25 = 75  cookies.


ANSWER.  Lauri did baked 75 cookies at first.

Solved.