At a concert 2/5 of the people were men, there were 3 times as many women as children. If there were 45 more men than children, how many people were there at the concert.

Final answer:

In solving the question, we establish two equations based on the condition provided, including the ratios among men, women, and children. Solving the equation, we find out that there were 270 people at the concert.

Explanation:

This question relates to the mathematical concept of ratio and proportion as well as fraction.

According to the question, 2/5 of the attendees at the concert were men and men outnumbered children by 45. First, let's make the number of children, x. So, the number of men will be x + 45. Because 2/5 of the total attendees were men, set up the equation: 2/5 * Total = x + 45.

There were 3 times as many women as children, thus the number of women will be 3x. So, the total number of people in the concert is the sum of the men, women, and children, which is (x + 45) + 3x + x. Simplifying this, we get 5x + 45 = Total. Therefore, if we substitute (x + 45) for 2/5 of the total in our original equation, we have 2/5 * (5x + 45) = x + 45. Solving this equation, we get x = 45.

So, if we substitute x=45 into our total equation, we get Total = 5(45) + 45 = 270. Therefore, there were 270 people at the concert.

Learn more about Ratio and Proportion here:

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This involves creating some equations.

First, these are what the letters I used stand for:

c = children

w = women

m = men

x = total population

Then, we must make an equation for each statement.

2/5x = m (2/5 of the people are men)

3c = w (there are 3 times as many women than children)

45+c = m (there are 45 more men than children)

Now, let's start plugging in our numbers:

x = all the men, women, and children

2/5(m+w+c) = m

2/5 (45+c +3c + c) = m     [Now simplify]

2/5 (45 + 5x) = m       [Now Distribute]

2/5(45) + (2/5)(5x) = m

2c + 18 = m    [Above we stated that there were the same amount as men as c +45]

2c + 18 = 45 +c     [Now set equal to c]

2c (-c) +18 = 45 +c (-c)

c+18 (-18) = 45 (-18)

c = 27

Now that we know that there was 27 children, we can plug 27 in for c in the other equations.

MEN = 27 + 45

WOMEN = 3(27)

CHILDREN = 27

Now add those three answers to find your total!