Question

Of the 800 participants in the marathon, 120 are running tp raise money for a cause. How many participants out of 100 are running for a cause

Answer 1

15 participants out of 100.

Explanation:

Using the numbers given, we can set up a ratio or proportion. We know that out of 800 participants, 120 are running for a cause. So we know that the part to whole ratio is 120:800, otherwise modeled as 120/800.

Method 1:

We need to manipulate this fraction in order to get the denominator to be 100 (since the whole needs to be 100 in this case).

To get from 800 to 100, we need to divide by 8. So we need to do
`(120)/(800)`÷
`(8)/(8)`

120/8 is 15, and 800/8 is 100. So we get our new simplified fraction of
`(15)/(100)`, which can also be modeled as 15:100 (part to whole).

Method 2:

Using the information we have, we can set up a proportion:

`(120)/(800) = (x)/(100)`

Now, we use this equality to find the value of x.

You can solve this proportion in multiple ways. The first way is very similar to what we did in the first method: we just say that 100 multiplied by 8 is 800, so x multiplied by 8 is 120:

8x = 120

Divide by 8 on both sides:

x=15

We can also do cross multiplication, but in this case, it is harder than the other methods:
800x = 12,000

Divide by 800 on both sides:

x = 15

Let me know if you have any questions.