Question 1210594
.
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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


                                  P a r t     1


<pre>
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

    {{{(3/4)x}}} = {{{5/2}}}  hours.


where x is the time under the question 1.

To find x, divide equation (1) by  {{{3/4}}}.  You will get

    x = {{{((5/2))/((3/4))}}} = {{{(5*4)/(2*3)}}} = {{{20/6}}} = {{{10/3}}} = 3 1/3 hours or 3 hours and 20 minutes.


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

Thus part (1) is completed.


<pre>
            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.
</pre>