+129852 The sum of two consecutive integers is no more than 209.
What is the larger of the two integers?
N + N +1 ≤ 209
2N + 1 ≤ 209 subtract 1 from both sides
2N ≤ 208 divide both sides by 2
N ≤ 104
The larger of the two integers = N + 1 = 105
A figure skater needs a total score of at least 90 to move on to the next round. The total score is the average of four judges’ scores. The first three judges’ scores were 83, 88, and 92. The figure skater made it to the next round.
What is the minimum score the fourth judge could have given?
We have that
[ 83 + 88 + 92 + M ] / 4 ≥ 90 multiply both sides by 4
83 + 88 + 92 + M ≥ 360 simplify
263 + M ≥ 360 subtract 263 from both sides
M ≥ 97 → the skater needs to get a score of 97 [or more ]
