## Algebra January 5, 2018May 29, 2021 The other day I got to use algebra to show my youngest how we could determine the shelf spacing on an Ikea shelf by only knowing it’s height and the height of another in the same family.

She was looking at this Mulig shelf unit for her new turntable and wanted to know if the shelves were tall enough for the records.  All we knew was that it was 35.375″ tall.  However, they have other units in the same family and this one is the same width and is 5 shelves instead of 3 and it’s 63.75″ tall.  With a couple of rational assumptions and some algebra we determined that it would work.

First the assumptions:

1. They are made from the same components.
2. The shelf spacing is the same between the two units.
3. The space above the top shelf and the space below the bottom shelf is equal.

Given that, once can write the following with X being the center to center spacing of the shelves and Y the space at the top and bottom:

4x+2y=63.75

2x+2y=35.375

Solving one for 2y we get:

2y=35.375-2x

Which we can then substitute in the first equation and solve for X:

4x+(35.375-2x)=63.75

2x+35.375=63.75

2x=28.375

x=14.1875

That then lets us solve for Y:

2y=35.375-2x

2y=35.375-2*14.1875

2y=35.375-28.375

2y=7

y=3.5

So, the shelf to shelf dim should be about 14.1875″ and the shelf center to floor dim should be about 3.5″.  Assuming a shelf thickness of about 1″, reasonable looking at the images, I estimated the open space to be 13.1875″. Plenty of space for 12″ records, so we ordered one.

After picking it up and putting it together I measured the space and found it was exactly what the algebra told us it would be – 13.1875″.

Gotta love math.