At a party one hundred and twenty people danced. The girls all started dancing one after the other. Tina was first girl who danced with seven men,Reena the second girl who danced with eight men, Sheela the third girl who danced with nine and so on up to Raveena who danced with all the men present. How many men were present at the party ?
number of men --- m
number of girls --- g
m+g = 120
Tina danced with 7 men
Reena danced with 8 men
....
Raveena danced with 120-g men
this is an arithmetic sequence with a=7, d=1
term(g) = m
a + (g-1)d = m
7 + g-1 = m
g - m = -6
also g+m = 120
add them
2g = 114
g = 57
m = 120-57 = 63
There were 63 men and 57 girls
check:
last girl should have danced with 63 men
---> last term = 63
term (57) = a + 56d = 7 + 56(1) = 63
YEahhh!
thankyou so much
To solve this problem, we first need to find the pattern in the number of men each girl danced with.
From the given information, we know that Tina was the first girl and danced with 7 men, Reena was the second girl and danced with 8 men, Sheela was the third girl and danced with 9 men, and so on.
We can observe that the number of men each girl danced with increases by 1 for each subsequent girl. This means that Tina is the first girl and danced with 7 men, Reena is the second girl and danced with 8 men (1 more than Tina), Sheela is the third girl and danced with 9 men (1 more than Reena), and so on.
The formula to find the number of men each girl danced with is:
Number of men for the nth girl = Starting number of men + (n - 1)
Now, we need to find the number of men for the last girl, Raveena, who danced with all the men present at the party. Since Raveena is the last girl, the number of men she danced with is equal to the total number of men present at the party.
So, we can use the formula to find the number of men Raveena danced with:
Number of men for Raveena = Starting number of men + (Total number of girls - 1)
In this case, the starting number of men is 7 (since Tina danced with 7 men), and the total number of girls is 120 (as given in the question).
Number of men for Raveena = 7 + (120 - 1) = 7 + 119 = 126
Therefore, there were 126 men present at the party.