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.

Step-by-step 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

Step-by-step 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 =$\dfrac{x}{2}$

Remaining exercise = $x-\dfrac{x}{2}=\dfrac{x}{2}$

The number of exercises she did while waiting for a friend after school=$\dfrac{2}{3}\times\dfrac{x}{2}=\dfrac{x}{3}$

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

Then, we have

$x=\dfrac{x}{2}+\dfrac{x}{3}+3\\\\\Rightarrow\ x-\dfrac{x}{2}-\dfrac{x}{3}=3\\\\\Rightarrow\dfrac{6x-3x-2x}{6}=3\\\\\Rightarrow\dfrac{x}{6}=3\\\\\Rightarrow\ x=6\times3=18$

Hence, she had 18 exercises for homework.