Question 1204475
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Answer: <font color=red size=4>29.4 cm</font>
This decimal value converts to the mixed number 29 & 2/5 which can be written as {{{matrix(1,2,29,2/5)}}}



Explanation


I'll convert each of the given mixed numbers into decimal form
78 & 2/5 = 78.4
12 & 1/2 = 12.5
2 & 3/5 = 2.6
4 & 1/2 = 4.5
Each result is exact


We start with 78.4 cm to work with. Two paintings take up 2*12.5 = 25 cm of horizontal space. 
Then we also have the 2.6 cm gap between those paintings to have a total of 25+2.6 = 27.6 cm so far.


The remaining horizontal space is 78.4 - 27.6 = 50.8 cm
Split this in half to get 25.4 cm buffer gaps on either side.


Refer to this diagram
*[illustration Screenshot_333.png]
The red segments are the two paintings.


Let point A be located at 0 on the number line.
Point B is at 25.4 on the number line.
C is at 25.4+12.5 = 37.9 on the number line.
The midpoint of B and C is (B+C)/2 = (25.4+37.9)/2 = 31.65 which is the horizontal center location of the first painting.


Or we could start at B = 25.4 and move 12.5/2 = 6.25 cm to the right to arrive at 25.4+6.25 = 31.65



From 31.65 on the number line, move (4.5)/2 = 2.25 cm to the left to arrive at 31.65-2.25 = <font color=red size=4>29.4 cm</font> which is the location of the first nail.


A similar question is found here
<a href = "https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1204434.html">https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1204434.html</a>
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