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. Which of the following is closest to the ratio of yellow jelly beans to all beans in the bowl?

$31\%$

$32\%$

$33\%$

$35\%$

$95\%$

Solution:

There are $26 \cdot .5 = 26 \div 2 = 13$ yellow jelly beans in the first bag, $28 \cdot .25 = 28 \div 4 = 7$ yellow jelly beans in the second bag, and $30 \cdot .2 = 30 \div 5 = 6$ yellow jelly beans in the third bag.

The total number of yellow jelly beans is $13 + 7 + 6 = 26$ and the total number of jelly beans is $26 + 28 + 30 = 84.$ The ratio of yellow jelly beans to all the beans is $\dfrac{26}{84} \cdot 100 \% = \dfrac{13}{42} \cdot 100 \%$ $\approx 30.9 \%.$

Thus, A is the correct answer.

1997 AMC 8 Problem 13

Solution:

Problem 13 in Other Years