Question

Three-fourths of a number increased by one-half is equal to fourteen. Find the number.

Answer 1

Okay the number 1/2 of 14 = 7 so then 3/4 of 7= 5 1/4 is the number.

Answer 2

18

Explanation:

First lets put your problem into an equation. It says that 3/4 a number, so we know that the first part of the equation is 3/4 times x:

`((3)/(4))(x)=\dfra{3}{4}x`

It says increased by 1/2 which means 1/2 is added because that's what increased means:

`(3)/(4)x+(1)/(2)`

Next it says all that is equal to 14. So now we put this in the end of our equation:

`(3)/(4)x+(1)/(2)=14`

Now that we have our equation we can solve for what x is:

`(3)/(4)x+(1)/(2)=14\\(3x)/(4)+(1)/(2)=14\\(3x)/(4)=14-(1)/(2)\\(3x)/(4)=(27)/(2)`

`(3x)(2)=(27)(4)\\ 6x=108`

`x=(108)/(6)`

`x=18`

So the answer would be 18.

If you are dealing with fractions, you should show it this way. There is an easy way though, if you convert all your fractions into decimals you can get the same answer.

`0.75x+0.5=14\\ 0.75x=14-0.5\\ 0.75x=13.5`

`x=(13.5)/(0.75)`

`x=18`