Question 1204434
<pre>
On a wall {{{78}}} {{{2/5}}} cm wide, Peter is going to hang five pictures beside each other, each measuring {{{12}}} {{{1/2}}} cm wide. He will leave {{{2}}} {{{3/5}}} cm in between each pair of adjacent pictures. He plans to use two nails to hang each picture and will centre these nails leaving {{{4}}} {{{1/2}}} cm between each pair. How far, in cm, from the end of the wall (on either side) will the first nail be placed?


I think a diagram is in order, so this can be better understood. *[illustration ADC_1204434_4.png].
I'll keep every measurement in fractional-form, to make it easy for ME to provide an answer 


As there are 5 pictures, there will be 5 - 1 or  4 spaces between the pics.
With space between each pic. being {{{matrix(1,2, 2&3/5, cm)}}}, total space between the 5 pics. is, {{{matrix(1,6, 4(2&3/5), "=", 8(12/5), "=", 10&2/5, cm)}}}
Total space for the 5 pics: {{{matrix(1,8, 5(12&1/2), "=", 5(12) + 5(1/2), "=", 60 + 2&1/2, "=", 62&1/2, cm)}}}
Total horizontal-space occupied by the 5 pics., separated by {{{matrix(1,2, 2&3/5, "-cm")}}}spaces: {{{matrix(1,6, 10&2/5 + 62&1/2, "=", 10&4/10 + 62&5/10, "=", 72&9/10, cm)}}}
Total space REMAINING in the allotted {{{matrix(1,2, 78&2/5, cm)}}} space: {{{matrix(1,10, 78&2/5 - 72&9/10, "=", 78&4/10 - 72&9/10, "=", 77&14/10 - 72&9/10, "=", 5&5/10, or, 5&1/2, cm)}}}
Space to the RIGHT of the left-side of the wall where the 1<sup>st</sup> of the 5 pics should be placed: {{{matrix(1,8, (5&1/2)/2, "=", (11/2)(1/2), "=", 11/4, "=", 2&3/4, cm)}}}. This is also the space to the LEFT of the right-side of the wall where the 5<sup>th</sup> 
or last of the 5 pics, should be placed.

 
Now, it would be a good time to check to see if ALL {{{matrix(1,2, 78&2/5, cm)}}} of space will be occupied. For this,
we get: {{{matrix(1,8, 10&2/5 + 62&1/2 + 2(2&3/4), "=", 10&2/5 + 62&1/2 + 5&1/2, "=", 10&2/5 + 68, "=", 78&2/5, cm)}}}. This CHECKS!!


From what I understand, 2 nails will be used to hang each pic, and the 2 nails will be CENTERED behind each pic., 
so that each pair of nails - behind each pic. - will be {{{matrix(1,2, 4&1/2, cm)}}} from each preceding and each succeeding pair of nails.
This means that the space between the 2<sup>nd</sup> of the 1<sup>st</sup> pair of nails and the 1<sup>st</sup> nail of the 2<sup>nd</sup> pair will be {{{matrix(1,2, 4&1/2, cm)}}} apart. 

With space between pics. being {{{matrix(1,2, 2&3/5, cm)}}}, remaining space between each pair of nails = {{{matrix(1,8, 4&1/2 - 2&3/5, "=", 9/2 - 13/5, "=", 45/10 - 26/10, "=", 19/10, cm)}}}
Therefore, space on EITHER side of the space between each pic. = {{{matrix(1,6, (19/10)/2, "=", (19/10)(1/2), "=", 19/20, cm)}}}

Finally, <font color = red><font size = 4><b>the 1<sup>st</sup> nail should be placed</font></font></b> {{{matrix(1,2, 19/20, cm)}}} to the right of the {{{matrix(1,2, 2&3/4, cm)}}} point from the left-side of the wall, or {{{matrix(1,9, 2&3/4 + 19/20, "=", 11/4 + 19/20, "=", 55/20 + 19/20, "or", 74/20, "=", highlight(highlight_green(highlight(matrix(1,4, 3&14/20, or, 3&7/10, cms)))))}}} <font color = red><font size = 4><b>from the left side of the wall</font></font></b>. This is the same for the right-side of the wall, also!!


All/Most of this might be confusing, but should be much clearer after the above diagram is viewed.</pre>