Question 1203188
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A bakery baked 1200 cupcakes and packed them into boxes.   
There were 5/8 as many big boxes as small boxes. 
Each big box contained 7 more cupcakes than each small box. 
There were 240 more cupcakes packed in big boxes than in the small boxes. 
How many cupcakes were there in each small box?
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The problem is to solve in two steps.


<pre>
        <U>First step</U>


Total x cupcakes packed in big   boxes
total y cupcakes packed in small boxes

From the problem

    x + y = 1200    (1)
    x - y =  240    (2)

Add equations (1) and (2).  You will get

    2x = 1440  -->  x = 1440/2 = 720              (the number of cupcakes packed in big boxes)

Then from eq(1)  y = 1200 - x = 1200 - 720 = 480  (the number of cupcakes packed in small boxes).
     

        <U>Second step</U>


Let z be the number of cupcakes in each small box (= the value under the problem's question)
Then the number of cupcases in each big box is (z+7).


The number of small boxes is {{{480/z}}}        (3)

The number of big   boxes is {{{720/(z+7)}}}   (4)


According to 5the problem, the ratio of the number of big boxes (4)
to the number of small boxes (3) is 5/8

   {{{((720/(z+7)))/((480/z))}}} = {{{5/8}}}.


Simplify and find z

    {{{(3*z)/(2*(z+7))}}} = {{{5/8}}}

    3z*8 = 5*2*(z+7)

    24z  = 10z + 70

    24z - 10z = 70

        14z   = 70

          z   = 70/14 = 5.


<U>ANSWER</U>.  The number of cupcakes in each small box is 5 (five).
</pre>

Solved.