Answer: One vase should be placed 3 feet from the end of the mantel and the other vase should be placed 9 feet from the same end.
Step-by-step explanation:
You know that lenght of the mantel above their fireplace is 12 feet.
They want to place one vase [tex]\frac{1}{4}[/tex] of the distance from one end of the mantel. This distance in feet is:
[tex]distance_{vase1}=(12feet)(\frac{1}{4})\\\\distance_{vase1}=3feet[/tex]
 They want to place the other vase [tex]\frac{3}{4}[/tex] of the distance from the same end of the mantel. Therefore, this distance in feet is:
[tex]distance_{vase2}=(12feet)(\frac{3}{4})\\\\distance_{vase2}=\frac{36feet}{4}\\\\distance_{vase2}=9feet[/tex]
Therefore, one vase should be placed 3 feet from the end of the mantel and the other vase should be placed 9 feet from the same end.
