A graphic designer is planning the layout for a magazine advertisement of three pictures, shown below. The ratio of the sum of the widths of the three pictures to the total width of the advertisement is 4:5. If each picture is 4 inches wide, what is the length of each of the four empty spaces between the pictures (t)?

The length of each space is 3/4 in.

Let S be the sum of the width of the pictures and T be the total width of the advertisement.  Our proportion would be
[tex]\frac{S}{T}=\frac{4}{5}[/tex]

Since there are 3 pictures and each is 4 inches long, S=3*4=12:
[tex]\frac{12}{T}=\frac{4}{5}[/tex]
Cross multiplying, we have:
12*5=4*T
60=4T
Divide both sides by 4:
60/4 = 4T/4
15=T
The total width of the advertisement is 15 inches.  Subtract the known width of the pictures from this, 12, and we have 3 inches left over for the total of the 4 spaces.  Thus our answer is 3/4.