Question

Marsha has some math exercises to do for homework. She did one half during study period and two thirds of those remaining while waiting for a friend after school. He had three to finish at home that evening. How many exercises did she have for homework?

Answer 1

Answer: She has 1 5/6 exercises for homework.

Explanation:

1/2 + 2/3 = 1 1/6

2 * 3 = 6 3 * 2 = 6

1 * 3 = 3 2 * 2 = 4

4 + 3/ 3 + 3

7/6 = 1 1/6

So, she finished 1 1/6 of her problems.

3 - 1 1/6 = 1 5/6

3 - 1 = 2

2 - 1/6 = 1 5/6

Answer 2

Answer: 18

Explanation:

Let x represents the number of exercises she had for homework.

Then, the expression for the number of exercises she did during study period =
`(x)/(2)`

Remaining exercise =
`x-(x)/(2)=(x)/(2)`

The number of exercises she did while waiting for a friend after school=
`(2)/(3)*(x)/(2)=(x)/(3)`

Also, she had three to finish at home that evening.

Then, we have

`x=(x)/(2)+(x)/(3)+3\\\\\Rightarrow\ x-(x)/(2)-(x)/(3)=3\\\\\Rightarrow(6x-3x-2x)/(6)=3\\\\\Rightarrow(x)/(6)=3\\\\\Rightarrow\ x=6*3=18`

Hence, she had 18 exercises for homework.