what is the answer for this question?

Question

In a bag of mixed beans, you have 160 pinto beans and 40 kidney beans. Pinto beans have a mass of 1.45 grams; kidney beans have a mass of 1.68 grams. 

 

a. what is the percent abundance of pinto beans?

b. what is the percent abundance of kidney beans?

c. what is the average mass of mixed beans?

d. what is the mass of the entire bag of mixed beans?

Answer 1

For the percent abundance, we are looking for the count of beans of a particular type to that of the total.

1) Percent abundance of pinto beans --> 160 / (160 + 40) = 160/200 = 4/5 or 80%

2) Percent abundance of kidney beans --> 40/ (160 + 40) = 40/200 = 1/5 or 20%

Note the total percent abundance MUST be 100% so if we didn't do any calculation for the second question and we know there are ONLY 2 types of beans then we could have immediately gotten the answer of 20% from (100% - 80%).

The average mass is the "weighted" average of the percent abundance of beans...

3) Average mass of the mixed beans --> (1.45*160 + 1.68*40)/(160 + 40) = (232+67.2)/200 = 1.496 grams

The total mass of the mixed beans in the bag is nothing more than the weigh of each bean added together...

4) Total mass of mixed beans in the bag --> 1.45*160 + 1.68*40 = 299.3 grams