Question

8.42 Three bags of jelly beans contain 26,28 , and 30 beans. In each bag, the percent of the beans that are yellow is 50%, 25%, and 20%, respectively. All three bags of candy are dumped into one bowl. What percent of the beans in the bowl are yellow? Round your answer to the nearest integer.

Answer 1

Explanation:

Figure out the number of yellow beans in each bag:

Bag A: 0.5*26 = 13 beans

Bag B: 0.25*28 = 7 beans

Bag C: 0.2*30 = 6 beans

The total number of beans in the bowl: 26+28+30 = 84

Total number of yellow beans: 13+7+6 = 26

Percentage of yellow beans: 26/84 *100 = 30.9523

Rounded answer: 31%

Answer 2

The percentage of yellow beans in the bowl of 84 is approximately 31%.

Explanation:

• We are given with a word problem
• We are asked to find the total percentage of yellow jelly beans
• We can do this two steps

Step 1: Finding the number of yellows beans in each bags

Step 2: Finding the total percentage of yellow beans

Step 1 of 2

We are given that the three bags contain 26,28 and 30 beans totally in which the percent of yellow beans are 50%, 25% and 20% respectively.

We have to find the number of yellow beans in each bag.

`$=(50)/(100) * 26$$`

The number of yellow beans in first bag

`$$\begin{aligned}&(1)/(2) * 26=13 \\&=(25)/(100) * 28\end{aligned}$$`

The number of yellow beans in second bag

`$$\begin{aligned}&(1)/(4) * 28=7 \\&=(20)/(100) * 30 \\&(1)/(5) * 30=6\end{aligned}$$`

The number of yellow beans in third bag

Step 2 of 2

From the first step we got the number of yellow beans in each bags.

The total number of yellow beans in the bowl =13+7+6

The total number of beans in the bowl

`$$\begin{aligned}=26 &+28+30 \\=& 84 \\&=(26)/(84) * 100\end{aligned}$$`

The percentage of yellow bean in the bowl

`$$\begin{gathered}\approx 0.3095 * 100 \\\approx 0.31 * 100 \\\approx 31\end{gathered}$$`