Question 1210594
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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?
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This author would like to chime in on this problem.

<font color = red><font size = 3><u>PART 2.</u></font></font>

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 {{{1/2}}}, the fraction of bracelets remaining was {{{1 - 1/2}}} = {{{1/2}}}
So, number of bracelets remaining was {{{(1/2)2x = x}}} 

Likewise, with the fraction of cookies sold being {{{3/5}}}, the fraction of cookies remaining was {{{1 - 3/5}}} = {{{2/5}}}
So, number of cookies remaining was {{{(2/5)5x = 2x}}}
 
With the remaining number of cookies being 48, or 2x, we get the following REMAINING
NUMBER-of-cookies equation: 2x = 48
                                                                                                               
<font color = red><font size = 3>Number of bracelets remaining (same as multiplicative factor) or {{{x = 48/2 = highlight(24)}}}</font></font>

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 {{{3/5}}} of cookies sold, number of cookies remaining = {{{1 - (3/5)5}}}, or {{{(2/5)5}}}, or 2 parts
With {{{1/2}}} of bracelets sold, number of bracelets remaining {{{1 - (1/2)2}}}, or {{{(1/2)2}}}, or 1 part

Now, we have 3 parts remaining and a cookies-to-bracelets ratio of 2:1
This puts the remaining cookies at {{{2/(2 + 1) = 2/3}}}, and remaining bracelets at {{{1/(2 + 1) = 1/3}}}
As total remaining cookies were 48, we get the <font color = red><font size = 3>Remaining number of bracelets as: {{{48(1)/2 = highlight(24)}}}</font></font>

@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!!</font></font></font></b></font></font></pre>