writing an inequality

Question

a number multiplied by 2 3/5, decreased by 1/10 is greater than 3/4

Answer 1

Hi Nick, 

 

The trick with word problems is converting them into an equation.  If you do it step by step you will be successful every time.

 

The number is X.

 

It is multiplied by 2 3/5 which we will write as an improper fraction or 13/5 so we have 13 * X / 5

 

We decrease it by 1/10 or subtract 1/10 from it to give 13 * X / 5 - 1/10 (This is my interpretation of decreasing it by 1/10.  If the person had said decrease it by 10% I would have answered this the way that Jon P. has done)

 

and it is greater than 3/4 so

 

13 * X / 5 - 1/10 > 3/4  

 

We can solve it for X

 

13 * X / 5 - 1/10 > 3/4

13 * X / 5  > 3/4 + 1/10

13 * X / 5 > 17/20

 

X > 17/52

 

Answer 2

Call the number x.  So write exactly what it says:

 

x * 2 3/5 * (1 - 1/10) > 3/4

 

(When you decrease a number by a fraction, you are multiplying it by 1 minus that fraction.)

 

x * 2 3/5 * 9/10 > 3/4