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

Answer:

The fraction of customers who prefer natural finishing es $\frac{7}{40}$

Step-by-step 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 :

$C = \frac{1}{8}C +\frac{2}{5}C +\frac{3}{10}C + X$

$C-\frac{1}{8}C -\frac{2}{5}C-\frac{3}{10} C = X$

We apply common denominator 200:

$\frac{200 * C-1 * 25C-2 * 40C-20 * 3C}{200} = X$

$\frac{(200-25-80-60) C}{200} = X$

$X = \frac{35}{200} C$

We divide both terms of the fraction by 5 :

$X =\frac{7}{40}C$

The fraction of customers who prefer natural finishing es $\frac{7}{40}$

Answer 2

Answer: $\frac{7}{40}$

Step-by-step 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:

$1-\frac{1}{8}-\frac{2}{5}-\frac{3}{10}=\frac{7}{40}$