Time for making bracelets is  2 1/2 hours, or  5/2 hours.


It is 3/4 of the time baking cookies.


So, we write this equation

     =   hours.


where x is the time under the question 1.

To find x, divide equation (1) by  .  You will get

    x =  =  =  =  = 3 1/3 hours or 3 hours and 20 minutes.


ANSWER to question 1: Luka spent 3 1/3 hours, or 3 hours and 20 minutes, baking cookies.

            Actually, this part is pure arithmetical problem 
            and can be solved MENTALLY without using equations.


2 1/2 hours is 150 minutes.

It is 3/4 of the baking time.

So, 1/4 of the baking time is 1/3 of 150 minutes, which is 50 minutes.

Hence, the whole baking time is 4*50 = 200 minutes, which is the same 3 hours and 20 minutes as we got above.

So, solving arithmetically, you get the same answer.

Luka and his friends are preparing for a local bazaar. Luka spent 2 1/2 hours making friendship bracelets, which was
3/4 of the time he spent baking cookies. The ratio of the number of cookies he baked to the number of bracelets he
made was 5:2.
1. How many hours did Luka spend baking cookies?
2. If he sold 3/5 of his cookies and 1/2 of his bracelets, and he had 48 cookies left, how many bracelets did he have
remaining?
***********************************************
This author would like to chime in on this problem.

PART 2.

Let the multiplicative factor be x
As the ratio of the number of cookies to bracelets made was 5:2, the number of cookies and bracelets made, were 5x and 2x,
respectively
With the fraction of bracelets sold being , the fraction of bracelets remaining was  = 
So, number of bracelets remaining was  

Likewise, with the fraction of cookies sold being , the fraction of cookies remaining was  = 
So, number of cookies remaining was 
 
With the remaining number of cookies being 48, or 2x, we get the following REMAINING
NUMBER-of-cookies equation: 2x = 48
                                                                                                               
Number of bracelets remaining (same as multiplicative factor) or 

OR

A 5:2 ratio of the number of cookies to number of bracelets means that there were 5 parts cookies to 2 parts bracelets

With  of cookies sold, number of cookies remaining = , or , or 2 parts
With  of bracelets sold, number of bracelets remaining , or , or 1 part

Now, we have 3 parts remaining and a cookies-to-bracelets ratio of 2:1
This puts the remaining cookies at , and remaining bracelets at 
As total remaining cookies were 48, we get the Remaining number of bracelets as: 

@KMST is correct! This author misread "....and he had 48 cookies left" as, he had 48 cookies and bracelets left. Corrections
were made above, and now, 24 is the correct number of bracelets that remained, not 16, as was previously calculated.

Thanks to @KMST for responding, revealing this error!!