SOLUTION: Ethan is a car salesman. On Monday, he sells one third of the cars in the lot. On Tuesday, he sells one fourth of the remaining cars in the lot. If he sells half the cars remaining

Question 946020: Ethan is a car salesman. On Monday, he sells one third of the cars in the lot. On Tuesday, he sells one fourth of the remaining cars in the lot. If he sells half the cars remaining in the lot on Wednesday, what percentage of the original cars did he sell?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
1/3 of the cars were sold on monday.
that leaves 2/3 of the cars remaining in the lot on monday.

1/4 of the remaining cars are sold on tuesday.
1/4 * 2/3 = 2/12 = 1/6.
that leaves 2/3 - 1/6 = 4/6 - 1/6 = 3/6 = 1/2 of the cars remaining in the lot on tuesday.

1/2 of the remaining cars are sold on wednesday.
1/2 * 1/2 = 1/4.
that leaves 1/2 - 1/4 = 1/4 of the cars remaining in the lot on wednesday.

1/4 of the cars remaining on the lot on wednesday means he sold 3/4 of the cars between monday and wednesday.

3/4 = .75 * 100% = 75%.

he sold 75% of the cars between monday and wednesday.

to see if this is true, let's assume that he has 12 cars on the lot on monday.

we could have used any number, but i chose 12 because 12 is the least common multiple of 3 and 4 and 2.

this allows us to get integer answers to each part of the problem.

he starts with 12 cars.
he sells 1/3 of 12 on monday which means he is left with 8.
he sells 1/4 of 8 on tuesday which means he is left with 6.
he sells 1/2 of 6 on wednesday which means he is left with 3.

he started with 12 and he is left with 3.
that means he sold 9.
9/12 = .75 * 100% = 75%.

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