One group (A) contains 435 people. One-third of the people in group A will be selected to win $20 fuel cards. There is another group (B) in a nearby town that will receive the same number of fuel cards, but there are 298 people in that group. What will be the ratio of nonwinners in group A to nonwinners in group B after the selections are made?

The ratio of non-winners in group A is 3/5 and in group B is 527/579. And the ratio of non-winners in group A to non-winners in group B will be 78/527.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

People in group A = 130

People in group B = 579

People in group A that will be selected to win US$ 50 fuel cards = 2/5

People in group B that will be selected to win US$ 50 fuel cards = same amount that group A

2. What will be the ratio of non-winners in group A to non-winners in group B after the selections are made?

Group A

If winners are 2/5, non-winners will be 1 - 2/5

1 - 2/5 = 5/5 - 2/5 = 3/5

Now, let's calculate the number of winners:

2/5 * 130 = 52 winners ⇒ 78 non-winners

Group B

Number of winners = 52 (Same amount that group A)

Ratio of winners = 52/579

Ratio of non-winners = 1 - 52/579 = 579/579 - 52/579 = 527/579

The ratio of non-winners in group A is 3/5 and in group B is 527/579. And the ratio of non-winners in group A to non-winners in group B will be 78/527.