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1.Our basketball team has finished 75% of its season, during which we won 40% of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?

 

2.Jim, Kim, and Lenny are hiking. Lenny forgot to bring water. Jim brought 2 gallons of water and Kim brought  1  3/4 gallons of water. The three of them agree to divide all the water equally among them. Lenny gives $2 for the water he receives, which Jim and Kim agree to divide fairly between the two of them. How much money should Jim receive?

 Feb 16, 2020
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1)  If you don't want to get too deeply involved with fractions, assume that there are 100 games.

If they have finished 75% of the season, they will have played 75 games.

If they have won 40% of the games they have played, they will have won 40% of 75 games, which are 30 games.

This also means that they have lost 75 - 30  =  45 games.

Their record is now:  30 W  and  45 L

To have a final winning percentage, they will need to end with  50 W  and  50L.

So, they will need to win  20  games and lose only  5  games.

To win  20  out of the remaining  25  games, their winning percentage will have to be:  20 / 25 =  80%  of the remaining games.

This analysis will work no matter how many games were actually played.

 

2)  Since Jim brought  2  gallons and Kim brought  1.75  gallons, together they brought  3.75  gallons.

To divide this evenly:  3.75  divided by  3  means that each person would have  1.25  gallons.

So, Jim will have to give Lenny  0.75  gallons and Kim will have to give Lenny  0.50  gallons.

Of the total amount (0.75 + 0.50 = 1.25 gallons), Jim will give up 0.75 gallons:  0.75 / 1.25  =  0.60  (or 60%).

Kim will give up 0.50 gallons:  0.50 / 1.25  =   0.40  (or 40%).

Therefore, Jim should get 60% of $2.00, or $1.20

and Kim should get 40% of $2.00, or $0.80.

 Feb 16, 2020

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