Question

Marcia has 412 bouquets of flowers for centerpieces. She uses 8 flowers for each centerpiece. How many centerpieces can she make?

Answer 1

`51` centerpieces

Explanation:

If Marcia has `412` bouquets of flowers, where `8` flowers will go in each centerpiece, then divide `412` by `8` to determine the number of centerpieces.

`412color(white)(i)"flowers"-:(8color(white)(i)"flowers")/"centerpiece"`

Take the reciprocal of the second fraction and change the division sign to a multiplication sign.

`=412color(white)(i)"flowers"xx("centerpiece")/(8color(white)(i)"flowers")`

The units, "flowers," cancel each other out as they appear in the numerator and denominator as a pair.

`=412color(white)(i)color(red)cancelcolor(black)("flowers")xx("centerpiece")/(8color(white)(i)color(red)cancelcolor(black)("flowers"))`

`=412xx("centerpiece")/8`

Solve.

`=51.5color(white)(i)"centerpiece"`

However, Marcia cannot have `51.5` centerpieces because the `.5` in `51.5` literally represents the physical half a centerpiece, which is not possible. So if Marcia has extra flowers which cannot fully fill a centerpiece, then she can make only `51` centerpieces, since `8` flowers must fill a centerpiece.

`:.`, Marcia can make `51` centerpieces.