Question

The ratio of newspapers to magazines in a library is 5:4. After the number of magazines is doubled and the number of newspapers is increased by 30, there are an equal number of newspapers and magazines. How many of each are there after the additions?

Answer 1

Solving the given proportions and linear equation, we find that initially there were 50 newspapers and 40 magazines. After doubling the magazines and adding 30 newspapers, the library has 80 of each.

Step-by-step explanation:

The student is asking a mathematical question involving proportional relationships and linear equations. Given the initial ratio of newspapers to magazines as 5:4, we know that for every 5 newspapers, there are 4 magazines. The problem then states that the number of magazines is doubled and the number of newspapers is increased by 30, resulting in an equal number of newspapers and magazines.

Let the original number of newspapers be 5x and the number of magazines be 4x. After the changes, the new number of newspapers would be 5x + 30 and the new number of magazines would be 2(4x). Since they are equal after the changes, we set up the equation 5x + 30 = 2(4x).

Solving for x, we have:

5x + 30 = 8x

30 = 3x

x = 10

With x = 10, the original number of newspapers would be 5x = 50, and the original number of magazines would be 4x = 40. After doubling the magazines and adding 30 newspapers, there would be 80 magazines and 80 newspapers.