Question

A recent poll shows that Sandra currently has 68% of the voters, but is losing 1% of the voters each day. Ricardo has 32% of the voters, but is gaining 1% of the voters each day.

Write an inequality that can be used to find the number of days, n, Ricardo will have a greater percentage of the voters than Sandra.
a) 32n > 68n - 1
b) 32n + 1 > 68n
c) 32n + 1 < 68n
d) 68n - 1 < 32n

Answer 1

The correct inequality to determine when Ricardo will have a greater percentage of the voters than Sandra is 68n - 1 < 32n, meaning Ricardo will have more voters after more than 18 days.

Step-by-step explanation:

The question involves finding the inequality that determines after how many days, n, Ricardo will have a greater percentage of the voters than Sandra. To find this, we start with the given information that Sandra has 68% and Ricardo has 32%, with each day Sandra losing 1% and Ricardo gaining 1%. The percentage of voters for both, over n days, would be 68 - n for Sandra and 32 + n for Ricardo. To find out when Ricardo will have more voters than Sandra, we set up the inequality 32 + n > 68 - n. Solving for n gives us 2n > 36, which simplifies to n > 18. Therefore, the correct inequality is 68n - 1 < 32n, option (d).