harish1986
A baseball team’s season consists of playing 162 games. At a certain point in its season, the team has won 55 percent of the games it has played. The team then wins a certain number of consecutive games so that at the end of the winning streak, the team has won 58 percent of the games it has played. How many wins did the team have at the end of its winning streak?
a. 10
b. 14
c. 42
d. 77
e. 87
Percentage of games won at the end of the winning streak = 58% = 58/100 = 29/50
Since 29/50 of these games are won -- and the season consists of 162 games -- the total number of games at the end of the winning streak must be a MULTIPLE OF 50 LESS THAN 162.
The following approach is called ALLIGATION.
Winning percentage for the first part of the season = 55%
Winning percentage for the winning streak = 100%
Winning percentage for the MIXTURE of the first part and the winning streak = 58%
Let F = the first part and S = the streak
Step 1: Plot the 3 percentages on a number line, with the percentages for F and S on the ends and the percentage for the mixture in the middle.F 55--------58--------100 S
Step 2: Calculate the distances between the percentages.F 55---
3---58---
42---100 S
Step 3: Determine the ratio in the mixture.The ratio of F to S is equal to the RECIPROCAL of the distances in red.
F:S= 42:3 = 14:1
The sum of the parts of the resulting ratio = 14+1 = 15.
Implication:
The total number of games at the end of the winning streak must be not only a multiple of 50 less than 162 but also a multiple of 15.
Only 150 is viable.
Since 29/50 of these 150 games are won, we get:
29/50 * 150 = 87