When 17 is reduced by 2/3 of a number the result is 13. Find the number

Question

When 17 is reduced by 2/3 of a number the result is 13. Find the number

Answer 1

Hello Jennifer,

 

Word problems are the hardest part of algebra. You have to understand what certain words mean.

 

In your problem, the phrase 'a number' means that it is unknown. Since they are unknown we call them 'variables' and will usually give them a letter. Let's call this number 'x'.

 

What is being done to 17? Well, 17 'is reduced by' something. That means that 17 is being subtracted by something.

What is this something? The something is 2/3's our variable ('x'). So, to show this in an algebraic phrase we write:

 

17 - 2/3x

 

Seventeen minus 2/3's times 'x'

 

Now look at the phrase 'the result is'. That means the same thing as 'is equal to'

 

In algebra you use the equal sign = to show that something 'is equal to'.

 

So far we have the algebraic phrase:

 

17 - 2/3 x =

 

Finally, what is it equal to? It is the result. 'the result is 13' Put it all together we have a complete algebraic equation:

 

17 - 2/3 x = 13.

 

Now you can solve the equation by solving for 'x'.

1) Subtract 17 from both sides.

2) Combine like terms.

3) divide both sides by -2/3

 

Check you answer by putting the answer back into the original equation and simplify.

Answer 2

17-(2/3)x=13

-(2/3)x=-4

(2/3)x=4

2x=12

x=6