Can anyone explain how to do this ACT math question? The answer is supposed to be a, but I was confused by the reasoning behind it.

Three years ago, men made up two out of every three internet users in America. Today the ratio of male to female users is about 1 to 1. In that time the number of American females using the internet has grown by 30,000,000, while the number of males who use the internet has grown by 100%. By how much has the total internet-user population increased in America in the past three years?

a. 50,000,000
b. 60,000,000
c. 80,000,000
d. 100,000,000
e. 200,000,000

asked 22 Jan '16, 18:13

Sam_PrepScholar's gravatar image

Sam_PrepScholar
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For this problem, you'll need to solve a system of equations. Since males made up 2/3 of internet users initially, this means that there were twice the number of males as there were females (2/3 versus 1/3). We can use variables to indicate the number of male and female internet users at this time with the equation x/y = 2 where x represents the initial number of male users and y represents the initial number of female users.

Then, we can use different variables to represent the current number of male and female users. Since the ratio is now one to one, we can say x1 = y1 where x1 is the current number of male users and y1 is the current number of female users.

So the two equations we have now are:

x/y = 2

x1 = y1

Now, lets relate the variables in the first equation to the variables in the second equation based on the question. The number of female users grew by 30 million, so we can conclude that y1 = y + 30,000,000. The number of male users grew by 100%, meaning it doubled, so we can say that x1 = 2x.

Our two additional equations are:

y1 = y + 30,000,000

x1 = 2x

Remember now that question is asking how much the total internet-user population grew. We already know that the female population grew by 30 million, so we need to solve for x to see how much the male population grew and add the two numbers together. We can just take an equation and rewrite all the variables in terms of x.

We know that y1 = y + 30,000,000. From the second equation, y1 = x1, so we can also say that x1 = y + 30,000,000.

From the fourth equation, x1 = 2x, which means we can replace x1 with 2x. That gives us 2x = y + 30,000,000 or 2x - 30,000,000 = y.

Now we can solve for x using the first equation and replacing y with the x expression. We now have x/(2x - 30,000,000) = 2.

Simplifying this expression, x = 4x - 60 million, which means that 3x = 60 million and x = 20 million.

Adding on the increase of 30 million female internet users, we can conclude that the total increase does come out to choice a, 50 million people.

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answered 23 Jan '16, 09:39

Sam_PrepScholar's gravatar image

Sam_PrepScholar
1.4k172174182

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