+9664 Don't know how to do these questions......
1) A mother says to her daughter, "When I was your age, you were only 7. But when you become my age, I will be 88 years old. What is the present age of the mother and that of the daughter?
2) In a meeting, everyone shakes hands with another person. If the total number of shaking hands is 2016 times, how many people was in the meeting?
+36919 #1
Mom age = x
Daughter age = y
age difference = x-y
Now, the Daughter's age MINUS the age difference equals 7
y-(x-y) = 7 or 2y-x=7 (Equation 1)
AND the Mother's age PLUS the age difference is 88
x+(x-y) = 88 or 2x-y =88 ((Equation 2)
From equation 1 : x = 2y-7 Sustitute into equation 2
2(2y-7) - y =88 solve for y =34 = daughter's age
Equation 1 again 2y-x=7 2(34) - x = 7 x = 61= mom's age
+36919
#2 Not sure..... do you mean that everyone there shakes hands with eveyone else there?
+26376 2) In a meeting, everyone shakes hands with another person.
If the total number of shaking hands is 2016 times,
how many people was in the meeting?
Let n = people in the meeting
\(\begin{array}{|rcll|} \hline \frac{ n\cdot (n-1) } {2} &=& 2016\ \text{handshakes }\\ n\cdot (n-1) &=& 4032 \\ n^2-n &=& 4032 \\ n^2-n -4032 &=& 0 \\\\ n &=& \frac{1+\sqrt{1-4\cdot(-4032) } }{2} \\ n &=& \frac{1+\sqrt{ 16129 } }{2} \\ n &=& \frac{1+127 } {2} \\ n &=& \frac{ 128 } {2} \\ n &=& 64 \\ \hline \end{array}\)
