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: 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 =[tex]\dfrac{x}{2}[/tex]
Remaining exercise = [tex]x-\dfrac{x}{2}=\dfrac{x}{2}[/tex]
The number of exercises she did while waiting for a friend after school=[tex]\dfrac{2}{3}\times\dfrac{x}{2}=\dfrac{x}{3}[/tex]
Also, she had three to finish at home that evening.
Then, we have
[tex]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[/tex]
Hence, she had 18 exercises for homework.
