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The ratio of women to children at a certain party is 2 to 5 and the ratio of children to men is 3 to 4. If there are more than 13 and less then 20 women at the party, what is the number of men at the party?
- a)30
- b)45
- c)60
- d)75
- e)90
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The ratio of women to children at a certain party is 2 to 5 and the ra...
Given Information:
The ratio of women to children at the party is 2 to 5.
The ratio of children to men is 3 to 4.
There are more than 13 and less than 20 women at the party.
Calculations:
Let's assume the number of women, children, and men at the party to be 2x, 5x, and 4x, respectively.
According to the given ratios:
- Women to children ratio = 2x : 5x = 2 : 5
- Children to men ratio = 5x : 4x = 3 : 4
From the above ratios:
- Women to children to men ratio = 2 : 5 : 4
Since the total ratio is 2 + 5 + 4 = 11, the total number of people at the party is 11x.
Given that there are more than 13 and less than 20 women:
13 < 2x="" />< />
6.5 < x="" />< />
Finding the Number of Men:
To find the number of men at the party, we need to calculate the total number of people:
- Minimum number of women (2x) = 2 * 7 = 14
- Maximum number of women (2x) = 2 * 10 = 20
Total number of people at the party = 11 * 7 = 77 (minimum) to 11 * 10 = 110 (maximum)
Therefore, the number of men at the party will be:
Total number of people - (Number of women + Number of children)
= Total number of people - (2x + 5x)
= Total number of people - 7x
Substitute the minimum and maximum values:
77 - 14 (minimum number of women) = 63
110 - 20 (maximum number of women) = 90
Hence, the number of men at the party is between 63 and 90. The closest option is 60 men (Option C), which falls within this range.
The ratio of women to children at the party is 2 to 5.
The ratio of children to men is 3 to 4.
There are more than 13 and less than 20 women at the party.
Calculations:
Let's assume the number of women, children, and men at the party to be 2x, 5x, and 4x, respectively.
According to the given ratios:
- Women to children ratio = 2x : 5x = 2 : 5
- Children to men ratio = 5x : 4x = 3 : 4
From the above ratios:
- Women to children to men ratio = 2 : 5 : 4
Since the total ratio is 2 + 5 + 4 = 11, the total number of people at the party is 11x.
Given that there are more than 13 and less than 20 women:
13 < 2x="" />< />
6.5 < x="" />< />
Finding the Number of Men:
To find the number of men at the party, we need to calculate the total number of people:
- Minimum number of women (2x) = 2 * 7 = 14
- Maximum number of women (2x) = 2 * 10 = 20
Total number of people at the party = 11 * 7 = 77 (minimum) to 11 * 10 = 110 (maximum)
Therefore, the number of men at the party will be:
Total number of people - (Number of women + Number of children)
= Total number of people - (2x + 5x)
= Total number of people - 7x
Substitute the minimum and maximum values:
77 - 14 (minimum number of women) = 63
110 - 20 (maximum number of women) = 90
Hence, the number of men at the party is between 63 and 90. The closest option is 60 men (Option C), which falls within this range.
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Community Answer
The ratio of women to children at a certain party is 2 to 5 and the ra...
Let's assume the number of women at the party is 2x and the number of children is 5x. According to the given ratio, the number of men would be (5x * 4/3) = (20x/3).
We know that there are more than 13 and less than 20 women at the party. Let's check the range of possible values for x:
For more than 13 women: 2x > 13 x > 6.5
For less than 20 women: 2x < 20 x < 10
The only integer value of x that satisfies both conditions is x = 7.
So, the number of men at the party would be (20x/3) = (20 * 7/3) = 140/3 = 46.67 (approximately).
Since the number of men must be an integer, the closest integer to 46.67 is 47. Therefore, the number of men at the party is 47.
Hence, the correct answer is option C.
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The ratio of women to children at a certain party is 2 to 5 and the ratio of children to men is 3 to 4. If there are more than 13 and less then 20 women at the party, what is the number of men at the party?a)30b)45c)60d)75e)90Correct answer is option 'C'. Can you explain this answer?
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