Question

Jose needs to memorize words on a vocabulary list for French class. He has memorized 20 of the words, which is four-fifths of the list. How many words are on

the list?

Answer 1

25

Step-by-step explanation:

In order to solve this the easiest way you can use equivalent fractions.

`(4)/(5) = (20)/(?)\\`

Since 4 times 5 equals 20 we can multiply 5 times 5 to get our answer.

`(4)/(5) * (5)/(5) = (20)/(25)`

25 is the answer. But, if we couldn't have gotten to 20 through the multiplication we could use a proportion. That would look like the initial problem but instead of a "?" we would use a variable. I will use t for total.

`(4)/(5) = (20)/(t)\\`

So now we have our problem set up. The next step is to cross multiply. 4 by t and 5 by 20.

`4t = 5 * 20\\4t = 100\\`

And now we can solve it like a normal algebra problem.

`(4)/(4)t = (100)/(4)\\t = 25`

Either way, we get 25.