Question

Frank builds kitchen cabinets. He offers four different wood finishes. 1/8 of his customers choose dark walnut, 2/5 choose golden oak, and 3/10 choose cherry. The rest of the customers prefer a natural finish. What fraction of the customers choose the natural finish?

Answer 1

The fraction of customers who prefer natural finishing es
`(7)/(40)`

Explanation:

We call X the fraction of customers who prefer natural finishing and C the total number of customers.

We define the following equation that relates the variables X and C :

`C = (1)/(8)C +(2)/(5)C +(3)/(10)C + X`

`C-(1)/(8)C -(2)/(5)C-(3)/(10) C = X`

We apply common denominator 200:

`(200 * C-1 * 25C-2 * 40C-20 * 3C)/(200)  = X`

`((200-25-80-60) C)/(200)  = X`

`X = (35)/(200) C`

We divide both terms of the fraction by 5 :

`X =(7)/(40)C`

The fraction of customers who prefer natural finishing es
`(7)/(40)`

Answer 2

Answer:
`(7)/(40)`

Explanation:

There is 1 group of costumers. You know that:

- 1/8 choose dark walnut.

- 2/5 choose golden oak.

- 3/10 choose cherry.

Therefore,you must make the subtraction shown below to find the fraction of the customers choose the natural finish- Therefore, the result is:

`1-(1)/(8)-(2)/(5)-(3)/(10)=(7)/(40)`