In a group of 126 spectators the ratio of men to women was 3:4. What is the new ratio if 2 more men and 8 more women joined the group of spectators?
original number:
men -- 3x
women -- 4x
3x+4x = 126
7x=126
x = 18
so we had 54 men and 72 women
new count:
men = 56
women = 80
new ratio :
men : women = 56:80 = 7 : 10
To find the new ratio, we need to calculate the total number of men and women after the additional spectators join the group.
First, let's calculate the number of men in the group:
Total spectators = 126
Ratio of men to women = 3:4
Total ratio parts = 3 + 4 = 7
Number of parts representing each ratio part = 126 / 7 = 18
Number of men = Ratio parts for men * Number of parts representing each ratio part = 3 * 18 = 54
Next, let's calculate the number of women in the group:
Number of women = Ratio parts for women * Number of parts representing each ratio part = 4 * 18 = 72
Now, let's calculate the new ratio:
Total number of men after additional spectators = 54 + 2 = 56
Total number of women after additional spectators = 72 + 8 = 80
New ratio of men to women = 56:80
Therefore, the new ratio if 2 more men and 8 more women joined the group of spectators is 56:80.
To find the new ratio, we need to calculate the total number of men and women after 2 more men and 8 more women join the group.
Given that the original ratio of men to women is 3:4, we can express it as a fraction: 3/4.
Let's calculate the number of men and women based on this ratio. We can assign the number of men to be 3x and the number of women to be 4x, where x is a constant.
So, the total number of spectators in the original group is 3x + 4x = 7x.
Given that there are 126 spectators in total, we can write the equation: 7x = 126.
To solve for x, we divide both sides of the equation by 7:
(7x)/7 = 126/7,
x = 18.
Now, we can find the number of men and women in the original group:
Number of men = 3x = 3 * 18 = 54
Number of women = 4x = 4 * 18 = 72
After 2 more men join the group, the total number of men becomes 54 + 2 = 56.
After 8 more women join the group, the total number of women becomes 72 + 8 = 80.
Thus, the new ratio of men to women is 56:80.
In order to simplify this ratio, we need to find the greatest common divisor (GCD) of 56 and 80, which is 8.
Dividing both numbers by the GCD, we get:
56 ÷ 8 = 7,
80 ÷ 8 = 10.
Therefore, the simplified new ratio of men to women is 7:10.