Question

The average bee only produces one-eighth teaspoon of honey in its lifetime. Also it takes 60,000 honey bees to produce 100 lb of honey. how much does a teaspoon of honey weigh Express the answer in ounces?

Answer 1

`color(blue)(16/75" ounces")`

Explanation:

Since we are asked for the answer in ounces, we convert 100lb to ounces.

There are 16 ounces in 1lb, so:

`100xx16=1600oz`

If 60,000 bees produce `1600 "oz"`, then 1 bee produces:

`1"bee"=1600/60000=2/75"oz"`

If one bee produces `1/8"th"` of a teaspoon of honey, then it will take 8 bees to produce 1 teaspoon of honey. We know how much 1 bee produces in weight, so the total weight of a teaspoonful is:

`8xx2/75=16/75"oz"`

A teaspoon of honey weighs `16/75"oz"`

Answer 2

`16/75 " ounces"`

There is a temptation to use decimals. Rounding off decimals is not as accurate or precise as fractions.

Explanation:

Known: 16 oz = 1 pound.

`color(brown)("Initial condition")`

`color(green)((" weight of honey")/("count of bees") color(white)("d")->color(white)("d") (100" pound")/(60000" bees"))" ".......Ratio(1)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Answering the question")`

We require the weight produced by 1 bee so the count of bees in `Ratio(1)` needs to be reduced to 1.

`("pounds")/("bees") ->(100 -:60000)/(60000-:60000) = (color(white)("d")1/600color(white)("d"))/1`

Lets use a smaller unit of measurement (ounces)

`1/600xx16 = 2/75" ounces "color(red)(" produced by 1 bee")`

`color(red)("However, 1 bee produces "1/8" of a teaspoon.")`

Let the weight of 1 teaspoon's worth of honey be `x`

So `1/8xx x=2/75`

`x=8/1xx2/75 = 16/75 " ounces"`