Question

Three bags of jelly beans contain 26, 28, and 30 beans. The ratios of yellow beans to all beans in each of these bags are $50\%$, $25\%$, and $20\%$, respectively. All three bags of candy are dumped into one bowl. To the nearest percent, what is the percentage of yellow jelly beans in the bowl?

Answer 1

Answer: 31%

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Step-by-step explanation:

The first bag has 26 beans total. Since 50% are yellow, this means 0.50*26 = 13 beans are yellow. Let A = 13.

The second bag has 28 beans, of which 25% are yellow, so 0.25*28 = 7 are yellow. Let B = 7.

The last bag has 30 means and 20% are yellow. So 0.20*30 = 6 are yellow. Let C = 6.

Add A,B,C to get A+B+C = 13+7+6 = 26 yellow from all three bags out of 26+28+30 = 84 beans total.

The percentage of yellow overall is 26/84 = 0.3095 = 30.95% approximately, which rounds to 31%