Question

When you roast the coffee, it loses 12% of its weight. How much fresh coffee do you need in order to get 14 225 lb. of roasted coffee?

Answer 1

Alright, lets get started.

Let me first share my double, its 14.225 lb or 14225 lb written in question.

I am considering 14.225 lb.

Lets suppose we have x lb coffee before roasting.

As given in question, it loses 12 % of its weight while roasting.

Means the rest weight of coffee after roasting = x - x * 12%

the rest weight of coffee after roasting = x - 0.12 x

the rest weight of coffee after roasting = 0.88 x

As per given in question, the weight after roasting = 14.225 lb

Equalling both

0.88x = 14.225

Dividing by 0.88

0.88x / 0.88 = 14.225 / 0.88

x = 16.1647 lb

Means we need to get 16.1647 lb coffee in order to get 14.225 lb : Answer

Hope it will help.

If 14225 lb is written in question , then calculation will be

x = 14225/0.88 = 16164.77 lb

Hope it will help :)

Answer 2

Let
`f` be the weight of the fresh coffee, and
`r` be the weight of the roasted coffee. The equation described by the first sentence is

`r = f\cdot \cfrac{88}{100} = f\cdot \cfrac{22}{25}`

In this case, we know
`r` and want to solve for
`f`: the equation becomes

`14225 = f\cdot \cfrac{22}{25}`

To solve for
`f`, multiply both sides by 25/22:

`14225 \cdot \cfrac{25}{22}= f\cdot \cfrac{22}{25} \cdot \cfrac{25}{22}`

`f = 14225 \cdot \cfrac{25}{22} = \cfrac{355625}{22} \approx 16164.77`