Answer to Question #202360 in Calculus for someone

Question

Lorena is comparing the winning percentages of two baseball teams. The Scorpions have won 20

20 out of 35 games. The Iguanas have won 10 out of 34 games. There are x games remaining until the playoffs. Which rational equation correctly describes the event in which the Iguanas win y of the remaining games and reach the same winning percentage as the Scorpions?

Assume that the Scorpions do not win another game. 

• 10+x/34+x = 20/35+y
• 10+y/34+x = 20+y/35+x
• 10+y/34+y = 20+x/35+x
• 10+y/34+x = 20/35+x
• 10+y/34+x = 20+x/35+x

it's NOT: 10+x/34+x = 20/35+y

Answer 1

$\text{Given, Lorena is comparing the winning percentages of two baseball teams. The Scorpions have won 20 out of 35 games. The Iguanas have won 10 out of 34 games. There are x games remaining until the playoffs. In the remaining events, Scorpions wins 0 games and Iguanas win y and reach the same winning percentage as the Scorpions.}\\ \text{ Now, total games played by Scorpians is }35+x.\\ \text{ Number of games they win is 20 out of} (35+x).\\ \text{ Then, the percentage of winning} =\frac{20}{35+x}×100 \\\text{ total games played by Iguanas is} \space 34+x.\\ \text{ Number of games they win is} \frac{10+y}{34+x}.\\ \text{ Then, the percentage of winning} = \frac{10+y}{34+x}×100\\ \text{ At the end, both winning percentage is same.}\\ \text{ Therefore,}\\ \frac{20}{35+x}×100=\frac{10+y}{34+x}×100 \\ \frac{20}{35+x}=\frac{10+y}{34+x} \\ \text{ Thus, fourth option i.e., }\frac{10+y}{34+x} =\frac{20}{35+x} \text{ is the right option.}$