Question

At George Washington High School, the ratio of graduating seniors that go on to college compared to those who do not is 7:4. Last year, 28 students did not go on to college. How many students did?

Answer 1

Number of seniors that graduated is `49`

Explanation:

You can get the answer in two ways..

Method 1

Comparing the given..

`7:4 -> "ratios"`

`7 ->` Graduated seniors..

`4 ->` Seniors that was unable to graduate..

`28 ->` Number Seniors that was unable to graduate..

`x ->` Number of Seniors that graduated..

Hence comparing;

`4/28 = 7/x`

Cross multiplying;

`4 xx x = 7 xx 28`

`4x = 196`

`x = 196/4`

`x = 49`

Therefore, the number of seniors that graduated is `49`

Method 2

Using Ratios and Proportions..

Sum of their ratios is `7 + 4 = 11`

Looking for the total number of seniors;

`28 = 4/11 xx y`

Where, `y` represents the total number of seniors..

`28 = 4/11y`

Dividing both sides by `4/11`

`28 div 4/11 = (4/11y)/(4/11)`

`28 div 4/11 = (cancel(4/11)y)/cancel(4/11)`

`28 xx 11/4 = y`

`cancel28^7 xx 11/cancel4^1 = x`

`7 xx 11 = y`

`y = 77`

Now to find the number of seniors that graduated..

Let, `x` represent the number of seniors that graduates;

`x = 7/11 xx 77`

`x = 7/cancel11^1 xx cancel77^7`

`x = 7 xx 7`

`x = 49`

Therefore the number of seniors that graduated is `49`