Two candidates A and B are up for election. A is so popular that the number of votes for B is expected to be less than or equal to 10% of A's votes. If the total number of votes for both candidates is 110 , what is the minimum number of votes we could expect A to receive?
A + B = 110
B <= .1A
A+.1A >= A+B = 110
1.1A >= 110
A >= 100
So, 100 votes for A, 10 for B
Anything less than 100 for A will result in less than 10 for B, so we can't make it to 110 votes.
Martina received
38
of the
160
votes cast for class secretary. How many votes did she receive
To find the minimum number of votes we could expect Candidate A to receive, we need to consider the given information: the number of votes for Candidate B is expected to be less than or equal to 10% of Candidate A's votes.
Let's assume that Candidate A receives x votes.
According to the given condition, Candidate B's votes will be less than or equal to 10% of Candidate A's votes.
Therefore, the number of votes for Candidate B will be 0.1x or less.
Since the total number of votes for both candidates is 110, we can set up the equation:
x + 0.1x ≤ 110
Simplifying the equation:
1.1x ≤ 110
Dividing both sides of the equation by 1.1 to solve for x:
x ≤ 100
So, the minimum number of votes we could expect Candidate A to receive is 100 votes.